Edit Profile (opens in new tab) Bannai, Eiichi Co-Author Distance Author ID: bannai.eiichi Published as: Bannai, Eiichi; Bannai, E. External Links: MGP Documents Indexed: 162 Publications since 1969, including 2 Books and 6 Additional arXiv Preprints 3 Contributions as Editor · 3 Further Contributions Biographic References: 1 Publication Co-Authors: 82 Co-Authors with 119 Joint Publications 2,331 Co-Co-Authors all top 5 Co-Authors 49 single-authored 43 Bannai, Etsuko 13 Zhu, Yan 12 Ito, Tatsuro 9 Song, Sung-Yell 9 Tanaka, Hajime 7 Miezaki, Tsuyoshi 7 Zhao, Da 6 Munemasa, Akihiro 4 Oura, Manabu 4 Tagami, Makoto 4 Yu, Wei-Hsuan 3 Harada, Masaaki 3 Hoggar, Stuart G. 3 Ozeki, Michio 3 Shimabukuro, Osamu 3 Sloane, Neil James Alexander 3 Venkov, Boris B. 2 Bannai, Hideo 2 Ceccherini-Silberstein, Tullio G. 2 Conway, John Horton 2 Damerell, Robert Mark 2 Hao, Shen 2 Hirao, Masatake 2 Jaeger, François 2 Kim, Kyoung-tark 2 Koike, Masao 2 Kurihara, Hirotake 2 Lee, Chin-Yen 2 Leech, John 2 Nakasora, Hiroyuki 2 Norton, Simon Phillips 2 Odlyzko, Andrew M. 2 Okuda, Takayuki 2 Parker, Richard A. 2 Queen, Larissa 2 Sali, Attila 2 Sawa, Masanori 2 Scarabotti, Fabio 2 Shigezumi, Junichi 2 Solé, Patrick 2 Suda, Sho 2 Tolli, Filippo 2 Xiang, Ziqing 1 Abdukhalikov, Kanat S. 1 Bachoc, Christine 1 Blokhuis, Aart 1 Borcherds, Richard Ewen 1 Cameron, Peter Jephson 1 Coulangeon, Renaud 1 Delsarte, Philippe 1 Deza, Michel Marie 1 Dougherty, Steven T. 1 Frankl, Péter 1 Griess, Robert L. jun. 1 Haemers, Willem H. 1 Ibukiyama, Tomoyoshi 1 Ikuta, Takuya 1 Iwasaki, Shiro 1 Kahn, Jeff D. 1 Kawanaka, Noriaki 1 Kim, Ann Chi 1 Kojima, Koji 1 Kwok, Wing Man 1 Li, Zengti 1 Minashima, Shinri 1 Nakahara, Mikio 1 Nakata, Yoshifumi 1 Navarro, Gabriel 1 Pétermann, Yves-François S. 1 Praeger, Cheryl Elisabeth 1 Rizo, Noelia 1 Sato, Takahiro 1 Scott, Leonard L. 1 Seidel, Johan Jacob 1 Sekiguchi, Jiro 1 Shinohara, Masashi 1 Stanton, Dennis W. 1 Suprijanto, Djoko 1 Suzuki, Hiroshi 1 Takano, Kyoichi 1 Tanaka, Rie 1 Teranishi, Yasuo 1 Tiep Pham Huu 1 Wei, Hongzeng 1 Yamada, Hiromichi 1 Yamaki, Hiroyoshi 1 Yoshida, Tomoyuki 1 Yudin, Vladimir A. 1 Zhu, Lin 1 Zhu, Yinfeng all top 5 Serials 17 European Journal of Combinatorics 8 Journal of Algebra 8 Journal of the Mathematical Society of Japan 8 Osaka Journal of Mathematics 8 Graphs and Combinatorics 7 Discrete Mathematics 7 Journal of Combinatorial Theory. Series A 6 Journal of the Faculty of Science. Section I A 5 Journal of Algebraic Combinatorics 4 Kyushu Journal of Mathematics 4 RIMS Kokyuroku 3 Hokkaido Mathematical Journal 3 Designs, Codes and Cryptography 2 Archiv der Mathematik 2 Journal of Combinatorial Theory. Series B 2 Journal of the London Mathematical Society. Second Series 2 Journal of Number Theory 2 Memoirs of the Faculty of Science. Series A. Mathematics 2 Proceedings of the Japan Academy. Series A 2 The Quarterly Journal of Mathematics. Oxford Second Series 2 Combinatorica 2 Sugaku Expositions 2 The Electronic Journal of Combinatorics 2 Journal of Applied Mathematics and Computing 2 Proceedings of the Japan Academy 2 Advanced Studies in Pure Mathematics 2 Grundlehren der Mathematischen Wissenschaften 2 Journal of Physics A: Mathematical and Theoretical 2 Journal of the Faculty of Science. Section I 1 Communications in Algebra 1 IEEE Transactions on Information Theory 1 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 1 Advances in Mathematics 1 Annales de l’Institut Fourier 1 Ars Combinatoria 1 Canadian Journal of Mathematics 1 Funkcialaj Ekvacioj. Serio Internacia 1 Geometriae Dedicata 1 Journal of Approximation Theory 1 Journal of Combinatorics, Information & System Sciences 1 Michigan Mathematical Journal 1 Nagoya Mathematical Journal 1 Pacific Journal of Mathematics 1 Proceedings of the London Mathematical Society. Third Series 1 Sūgaku 1 Linear Algebra and its Applications 1 St. Petersburg Mathematical Journal 1 Izvestiya: Mathematics 1 Taiwanese Journal of Mathematics 1 Annals of Combinatorics 1 Moscow Mathematical Journal 1 Contributions to Discrete Mathematics 1 Lecture Notes in Mathematics 1 Proceedings of the Steklov Institute of Mathematics 1 Ars Mathematica Contemporanea 1 Japanese Journal of Mathematics. 3rd Series 1 Moscow Journal of Combinatorics and Number Theory 1 De Gruyter Series in Discrete Mathematics and Applications 1 Mathematics Lecture Note Series all top 5 Fields 119 Combinatorics (05-XX) 56 Group theory and generalizations (20-XX) 21 Information and communication theory, circuits (94-XX) 20 Number theory (11-XX) 13 Geometry (51-XX) 6 Convex and discrete geometry (52-XX) 6 Numerical analysis (65-XX) 5 Statistics (62-XX) 5 Quantum theory (81-XX) 4 Linear and multilinear algebra; matrix theory (15-XX) 3 General and overarching topics; collections (00-XX) 3 Special functions (33-XX) 3 Harmonic analysis on Euclidean spaces (42-XX) 3 Abstract harmonic analysis (43-XX) 3 Manifolds and cell complexes (57-XX) 3 Statistical mechanics, structure of matter (82-XX) 2 History and biography (01-XX) 2 Field theory and polynomials (12-XX) 2 Commutative algebra (13-XX) 2 Operations research, mathematical programming (90-XX) 1 Mathematical logic and foundations (03-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Associative rings and algebras (16-XX) 1 Nonassociative rings and algebras (17-XX) 1 Functions of a complex variable (30-XX) 1 Ordinary differential equations (34-XX) 1 Approximations and expansions (41-XX) 1 Probability theory and stochastic processes (60-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 147 Publications have been cited 2,342 times in 1,527 Documents Cited by ▼ Year ▼ Algebraic combinatorics. I: Association schemes. Zbl 0555.05019 Bannai, Eiichi; Ito, Tatsuro 914 1984 Sphere packings, lattices and groups. With additional contributions by E. Bannai, R. E. Borcherds, J. Leech, S. P. Norton, A. M. Odlyzko, R. A. Parker, L. Queen and B. B. Venkov. 3rd ed. Zbl 0915.52003 Conway, J. H.; Sloane, N. J. A. 590 1999 Sphere packings, lattices and groups. With additional contributions by E. Bannai, J. Leech, S. P. Norton, A. M. Odlyzko, R. A. Parker, L. Queen and B. B. Venkov. Zbl 0634.52002 Conway, J. H.; Sloane, N. J. A. 418 1988 A survey on spherical designs and algebraic combinatorics on spheres. Zbl 1207.05022 Bannai, Eiichi; Bannai, Etsuko 77 2009 On finite Moore graphs. Zbl 0275.05121 Bannai, Eiichi; Ito, Tatsuro 74 1973 Tight spherical designs. I. Zbl 0403.05022 Bannai, Eiichi; Damerell, Robert Mark 67 1979 Tight spherical designs. II. Zbl 0436.05018 Bannai, Eiichi; Damerell, Robert Mark 61 1980 Type II codes, even unimodular lattices, and invariant rings. Zbl 0958.94042 Bannai, Eiichi; Dougherty, Steven T.; Harada, Masaaki; Oura, Manabu 61 1999 Subschemes of some association schemes. Zbl 0762.20004 Bannai, Eiichi 42 1991 An upper bound for the cardinality of an s-distance subset in real Euclidean space. II. Zbl 0522.05022 Bannai, Eiichi; Bannai, Etsuko; Stanton, Dennis 37 1983 The nonexistence of certain tight spherical designs. Zbl 1072.05017 Bannai, E.; Munemasa, A.; Venkov, B. 31 2005 Generalized generalized spin models (four-weight spin models). Zbl 0848.05072 Bannai, Eiichi; Bannai, Etsuko 28 1995 Regular graphs with excess one. Zbl 0473.05036 Bannai, Eiichi; Ito, Tatsuro 24 1981 On Euclidean tight 4-designs. Zbl 1104.05016 Bannai, Eiichi; Bannai, Etsuko 22 2006 Codes and designs in Grassmannian spaces. Zbl 1040.05005 Bachoc, Christine; Bannai, Eiichi; Coulangeon, Renaud 22 2004 Type II codes over \(\mathbb F_2+ u\mathbb F_2\) and applications to Hermitian modular forms. Zbl 1048.11038 Bannai, Eiichi; Harada, Masaaki; Ibukiyama, Tomoyoshi; Munemasa, Akihiro; Oura, Manabu 22 2003 On spin models, modular invariance, and duality. Zbl 0880.05083 Bannai, Eiichi; Bannai, Etsuko; Jaeger, François 22 1997 Spin models on finite cyclic groups. Zbl 0803.05058 Bannai, Eiichi; Bannai, Etsuko 22 1994 The Terwilliger algebras of group association schemes. Zbl 0839.05095 Bannai, Eiichi; Munemasa, Akihiro 21 1995 Character tables of the association schemes of finite orthogonal groups acting on the nonisotropic points. Zbl 0762.20005 Bannai, Eiichi; Hao, Shen; Song, Sung-Yell 20 1990 Spherical designs of harmonic index \(t\). Zbl 1312.05030 Bannai, Eiichi; Okuda, Takayuki; Tagami, Makoto 19 2015 Association schemes and fusion algebras. (An introduction). Zbl 0790.05098 Bannai, Eiichi 19 1993 Current research on algebraic combinatorics. Supplements to our book, Algebraic combinatorics I. Zbl 0685.05030 Bannai, Eiichi; Ito, Tatsuro 19 1986 Maximal subgroups of low rank of finite symmetric and alternating groups. Zbl 0262.20003 Bannai, Eiichi 17 1972 The character table of the Hecke algebra \({\mathcal H}(GL_{2n}(\mathbb{F}_ q),Sp_{2n}(\mathbb{F}_ q))\). Zbl 0761.20013 Bannai, Eiichi; Kawanaka, Noriaki; Song, Sung-Yell 16 1990 Algebraic combinatorics. Translated from the Japanese. Originally published by Kyoritsu Shuppan (Kyoritsu Publisher), Tokyo 2016. Zbl 1472.05002 Bannai, Eiichi; Bannai, Etsuko; Ito, Tatsuro; Tanaka, Rie 16 2021 On distance-regular graphs with fixed valency. Zbl 0626.05050 Bannai, Eiichi; Ito, Tatsuro 16 1987 On tight t-designs in compact symmetric spaces of rank one. Zbl 0572.05018 Bannai, Eiichi; Hoggar, Stuart G. 16 1985 On tight designs. Zbl 0391.05005 Bannai, Eiichi 15 1977 Uniqueness of certain spherical codes. Zbl 0411.05028 Bannai, Eiichi; Sloane, N. J. A. 15 1981 Character tables of fission schemes and fusion schemes. Zbl 0794.05131 Bannai, Eiichi; Song, Sung Yell 15 1993 Remarks on the concepts of \(t\)-designs. Zbl 1296.05017 Bannai, Eiichi; Bannai, Etsuko 14 2012 Character tables of commutative association schemes. Zbl 0757.05100 Bannai, Eiichi 14 1990 On distance-regular graphs with fixed valency. II. Zbl 0699.05038 Bannai, Eiichi; Ito, Tatsuro 14 1988 On extremal finite sets in the sphere and other metric spaces. Zbl 0723.05113 Bannai, E. 14 1988 Spherical t-designs which are orbits of finite groups. Zbl 0545.05025 Bannai, Eiichi 14 1984 Association schemes related to universally optimal configurations, Kerdock codes and extremal Euclidean line-sets. Zbl 1250.05119 Abdukhalikov, Kanat; Bannai, Eiichi; Suda, Sho 13 2009 Finite analogues of non-Euclidean spaces and Ramanujan graphs. Zbl 1033.05099 Bannai, Eiichi; Shimabukuro, Osamu; Tanaka, Hajime 13 2004 Design theory from the viewpoint of algebraic combinatorics. Zbl 1365.05301 Bannai, Eiichi; Bannai, Etsuko; Tanaka, Hajime; Zhu, Yan 13 2017 On distance-regular graphs with fixed valency. IV. Zbl 0677.05061 Bannai, Eiichi; Ito, Tatsuro 12 1989 Cubature formulas in numerical analysis and Euclidean tight designs. Zbl 1227.05107 Bannai, Eiichi; Bannai, Etsuko; Hirao, Masatake; Sawa, Masanori 11 2010 Euclidean designs and coherent configurations. Zbl 1231.05019 Bannai, Eiichi; Bannai, Etsuko 11 2010 On relative \(t\)-designs in polynomial association schemes. Zbl 1329.05307 Bannai, Eiichi; Bannai, Etsuko; Suda, Sho; Tanaka, Hajime 11 2015 On distance-regular graphs with fixed valency. III. Zbl 0677.05060 Bannai, Eiichi; Ito, Tatsuro 11 1987 Construction of Jacobi forms from certain combinatorial polynomials. Zbl 0860.11026 Bannai, Eiichi; Ozeki, Michio 10 1996 Tight t-designs and squarefree integers. Zbl 0713.05009 Bannai, E.; Hoggar, S. G. 10 1989 On antipodal spherical \(t\)-designs of degree \(s\) with \(t\geq 2s-3\). Zbl 1270.05017 Bannai, Eiichi; Bannai, Etsuko 10 2009 How many P-polynomial structures can an association scheme have? Zbl 0458.94047 Bannai, Eiichi; Bannai, Etsuko 10 1980 A global study of Jordan-Pochhammer differential equations. Zbl 0349.34009 Takano, Kyoichi; Bannai, Eiichi 9 1976 On perfect codes in the Hamming schemes H(n,q) with q arbitrary. Zbl 0356.94008 Bannai, Eiichi 9 1977 Finite Euclidean graphs and Ramanujan graphs. Zbl 1208.05046 Bannai, Eiichi; Shimabukuro, Osamu; Tanaka, Hajime 9 2009 Spherical designs attached to extremal lattices and the modulo \(p\) property of Fourier coefficients of extremal modular forms. Zbl 1121.11046 Bannai, Eiichi; Koike, Masao; Shinohara, Masashi; Tagami, Makoto 9 2006 The character tables of Paige’s simple Moufang loops and their relationship to the character tables of PSL(2,q). Zbl 0682.20050 Bannai, Eiichi; Song, Sung-Yell 9 1989 Tight Gaussian 4-designs. Zbl 1069.05016 Bannai, Eiichi; Bannai, Etsuko 9 2005 Spherical designs and Euclidean designs. Zbl 1209.05266 Bannai, Eiichi; Bannai, Etsuko 8 2009 Tight relative 2- and 4-designs on binary Hamming association schemes. Zbl 1295.05275 Li, Zengti; Bannai, Eiichi; Bannai, Etsuko 8 2014 Tight relative 2-designs on two shells in Johnson association schemes. Zbl 1327.05347 Zhu, Yan; Bannai, Eiichi; Bannai, Etsuko 8 2016 On the existence of tight relative 2-designs on binary Hamming association schemes. Zbl 1277.05031 Bannai, Eiichi; Bannai, Etsuko; Bannai, Hideo 8 2014 On some spherical t-designs. Zbl 0464.05016 Bannai, Eiichi 8 1979 A note on the spherical embeddings of strongly regular graphs. Zbl 1071.05074 Bannai, Eiichi; Bannai, Etsuko 8 2005 Automorphisms of irreducible Weyl groups. Zbl 0196.05005 Bannai, E. 7 1969 Toy models for D. H. Lehmer’s conjecture. Zbl 1216.11048 Bannai, Eiichi; Miezaki, Tsuyoshi 7 2010 Relative \(t\)-designs in binary Hamming association scheme \(H(n,2)\). Zbl 1367.05027 Bannai, Eiichi; Bannai, Etsuko; Zhu, Yan 7 2017 On the strong non-rigidity of certain tight Euclidean designs. Zbl 1123.05024 Bannai, Eiichi; Bannai, Etsuko; Suprijanto, Djoko 7 2007 An upper bound for the cardinality of an s-distance subset in real euclidean space. Zbl 0491.05024 Bannai, Eiichi; Bannai, Etsuko 7 1981 Generalized spin models and association schemes. Zbl 0797.05082 Bannai, Eiichi; Bannai, Etsuko 7 1993 Classification of small spin models. Zbl 0823.05065 Bannai, Eiichi; Jaeger, François; Sali, Attila 7 1994 On spherical designs of some harmonic indices. Zbl 1361.05023 Zhu, Yan; Bannai, Eiichi; Bannai, Etsuko; Kim, Kyoung-Tark; Yu, Wei-Hsuan 7 2017 On primitive symmetric association schemes with \(m_1=3\). Zbl 1093.05073 Bannai, Eiichi; Bannai, Etsuko 6 2006 Codes in bipartite distance-regular graphs. Zbl 0365.94015 Bannai, Eiichi 6 1977 Doubly transitive permutation representations of the finite projective special linear groups PSL(n,q). Zbl 0253.20007 Bannai, Eiichi 6 1971 Character tables of certain association schemes coming from finite unitary and symplectic groups. Zbl 0824.20009 Bannai, Eiichi; Song, Sung-Yell; Hao, Shen; Wei, Hongzeng 6 1991 Unitary \(t\)-groups. Zbl 1485.20016 Bannai, Eiichi; Navarro, Gabriel; Rizo, Noelia; Tiep, Pham Huu 6 2020 Some results on modular forms – subgroups of the modular group whose ring of modular forms is a polynomial ring. Zbl 1029.11012 Bannai, Eiichi; Koike, Masao; Munemasa, Akihiro; Sekiguchi, Jiro 6 2001 The decomposition of the permutation character \(1^{\text{GL}(2n,q)}_{\text{GL}(n,q^2)}\). Zbl 1031.20040 Bannai, Eiichi; Tanaka, Hajime 6 2003 The study of distance-regular graphs from the algebraic (i.e., character theoretical) viewpoint. Zbl 0677.05059 Bannai, Eiichi; Ito, Tatsuro 6 1987 Orthogonal polynomials in coding theory and algebraic combinatorics. Zbl 0704.42025 Bannai, Eiichi 6 1990 Rigid spherical t-designs and a theorem of Y. Hong. Zbl 0718.05016 Bannai, Eiichi 6 1987 Uniqueness of certain association schemes. Zbl 1200.05258 Bannai, Eiichi; Bannai, Etsuko; Bannai, Hideo 5 2008 On optimal tight 4-designs on 2 concentric spheres. Zbl 1083.62067 Bannai, Eiichi; Bannai, Etsuko 5 2006 On tight spherical designs. Zbl 0425.05015 Bannai, Eiichi 5 1979 On the spectra of certain distance-regular graphs. Zbl 0427.15005 Bannai, Eiichi; Ito, Tatsuro 5 1979 On rank 3 groups with a multiply transitive constituent. Zbl 0241.20003 Bannai, Eiichi 5 1972 Toy models for D. H. Lehmer’s conjecture. II. Zbl 1310.11052 Bannai, Eiichi; Miezaki, Tsuyoshi 5 2013 An elementary approach to toy models for D. H. Lehmer’s conjecture. Zbl 1293.11067 Bannai, Eiichi; Miezaki, Tsuyoshi; Yudin, Vladimir A. 5 2011 Nonexistence of certain distance-transitive digraphs. Zbl 0468.05035 Bannai, Eiichi; Cameron, Peter J.; Kahn, Jeff 5 1981 On some subgroups of the group Sp(2n,2). Zbl 0261.20035 Bannai, Eiichi 4 1971 A note on characters of normal subgroups of multiply transitive permutation groups. Zbl 0285.20015 Bannai, Eiichi 4 1973 Tight \(t\)-designs on two concentric spheres. Zbl 1314.05230 Bannai, Eiichi; Bannai, Etsuko 4 2014 A survey on tight Euclidean \(t\)-designs and tight relative \(t\)-designs in certain association schemes. Zbl 1319.05025 Bannai, Eiichi; Bannai, Etsuko; Zhu, Yan 4 2015 The character table of the commutative association scheme coming from the action of \(GL(n,q)\) on non-incident point-hyperplane pairs. Zbl 0762.20003 Bannai, Eiichi; Song, Sung-Yell 4 1990 An introduction to association schemes. Zbl 0967.05068 Bannai, Eiichi 4 1999 Thoughts on modular forms. Zbl 0957.11500 Bannai, Eiichi 4 1999 On a property of 2-dimensional integral Euclidean lattices. Zbl 1236.11059 Bannai, Eiichi; Miezaki, Tsuyoshi 4 2012 Modular invariance of the character table of the Hamming association scheme \(H(d,q)\). Zbl 0799.05068 Bannai, Eiichi; Bannai, Etsuko 4 1994 Modular invariance property of association schemes, type II codes over finite rings and finite abelian groups and reminiscences of François Jaeger (a survey). Zbl 0917.05086 Bannai, Eiichi 4 1999 Harmonic index designs in binary Hamming schemes. Zbl 1387.05035 Zhu, Yan; Bannai, Eiichi; Bannai, Etsuko; Ikuta, Takuya; Kim, Kyoung-Tark 3 2017 The mathematics of Donald Gordon Higman. Zbl 1165.01309 Bannai, Eiichi; Griess, Robert L. jun.; Praeger, Cheryl E.; Scott, Leonard 3 2009 Latest topics in algebraic combinatorics and association schemes. Zbl 0794.05130 Bannai, Eiichi 3 1993 On the ring of simultaneous invariants for the Gleason-MacWilliams group. Zbl 0944.15022 Bannai, Eiichi; Bannai, Etsuko; Ozeki, Michio; Teranishi, Yasuo 3 1999 A note on the Assmus-Mattson theorem for some binary codes. II. Zbl 07698623 Bannai, Eiichi; Miezaki, Tsuyoshi; Nakasora, Hiroyuki 3 2023 Tight relative \(t\)-designs on two shells in hypercubes, and Hahn and Hermite polynomials. Zbl 1518.05029 Bannai, Eiichi; Bannai, Etsuko; Tanaka, Hajime; Zhu, Yan 3 2022 Algebraic combinatorics. Translated from the Japanese. Originally published by Kyoritsu Shuppan (Kyoritsu Publisher), Tokyo 2016. Zbl 1472.05002 Bannai, Eiichi; Bannai, Etsuko; Ito, Tatsuro; Tanaka, Rie 16 2021 The complex conjugate invariants of Clifford groups. Zbl 1458.15040 Bannai, Eiichi; Oura, Manabu; Zhao, Da 1 2021 Classification of spherical 2-distance \(\{4,2,1\}\)-designs by solving Diophantine equations. Zbl 1475.05021 Bannai, Eiichi; Bannai, Etsuko; Xiang, Ziqing; Yu, Wei-Hsuan; Zhu, Yan 1 2021 Unitary \(t\)-groups. Zbl 1485.20016 Bannai, Eiichi; Navarro, Gabriel; Rizo, Noelia; Tiep, Pham Huu 6 2020 Spherical embeddings of symmetric association schemes in 3-dimensional Euclidean space. Zbl 1436.05139 Bannai, Eiichi; Zhao, Da 1 2020 Gelfand triples and their Hecke algebras. Harmonic analysis for multiplicity-free induced representations of finite groups. With a foreword by Eiichi Bannai. Zbl 1479.20002 Ceccherini-Silberstein, Tullio; Scarabotti, Fabio; Tolli, Filippo 1 2020 Tight \(t\)-designs on one shell of Johnson association schemes. Zbl 1415.05183 Bannai, Eiichi; Zhu, Yan 2 2019 On the explicit constructions of certain unitary \(t\)-designs. Zbl 1509.81147 Bannai, Eiichi; Nakahara, Mikio; Zhao, Da; Zhu, Yan 2 2019 Half of an antipodal spherical design. Zbl 1386.05022 Bannai, Eiichi; Zhao, Da; Zhu, Lin; Zhu, Yan; Zhu, Yinfeng 3 2018 Design theory from the viewpoint of algebraic combinatorics. Zbl 1365.05301 Bannai, Eiichi; Bannai, Etsuko; Tanaka, Hajime; Zhu, Yan 13 2017 Relative \(t\)-designs in binary Hamming association scheme \(H(n,2)\). Zbl 1367.05027 Bannai, Eiichi; Bannai, Etsuko; Zhu, Yan 7 2017 On spherical designs of some harmonic indices. Zbl 1361.05023 Zhu, Yan; Bannai, Eiichi; Bannai, Etsuko; Kim, Kyoung-Tark; Yu, Wei-Hsuan 7 2017 Harmonic index designs in binary Hamming schemes. Zbl 1387.05035 Zhu, Yan; Bannai, Eiichi; Bannai, Etsuko; Ikuta, Takuya; Kim, Kyoung-Tark 3 2017 Tight relative 2-designs on two shells in Johnson association schemes. Zbl 1327.05347 Zhu, Yan; Bannai, Eiichi; Bannai, Etsuko 8 2016 Spherical designs of harmonic index \(t\). Zbl 1312.05030 Bannai, Eiichi; Okuda, Takayuki; Tagami, Makoto 19 2015 On relative \(t\)-designs in polynomial association schemes. Zbl 1329.05307 Bannai, Eiichi; Bannai, Etsuko; Suda, Sho; Tanaka, Hajime 11 2015 A survey on tight Euclidean \(t\)-designs and tight relative \(t\)-designs in certain association schemes. Zbl 1319.05025 Bannai, Eiichi; Bannai, Etsuko; Zhu, Yan 4 2015 Appendix: On some Gelfand pairs and commutative association schemes. Zbl 1346.20004 Bannai, Eiichi; Tanaka, Hajime 1 2015 Tight relative 2- and 4-designs on binary Hamming association schemes. Zbl 1295.05275 Li, Zengti; Bannai, Eiichi; Bannai, Etsuko 8 2014 On the existence of tight relative 2-designs on binary Hamming association schemes. Zbl 1277.05031 Bannai, Eiichi; Bannai, Etsuko; Bannai, Hideo 8 2014 Tight \(t\)-designs on two concentric spheres. Zbl 1314.05230 Bannai, Eiichi; Bannai, Etsuko 4 2014 Toy models for D. H. Lehmer’s conjecture. II. Zbl 1310.11052 Bannai, Eiichi; Miezaki, Tsuyoshi 5 2013 Combinatorics as pure mathematics – aims of algebraic combinatorics. Zbl 1388.05002 Bannai, Eiichi 1 2013 Remarks on the concepts of \(t\)-designs. Zbl 1296.05017 Bannai, Eiichi; Bannai, Etsuko 14 2012 On a property of 2-dimensional integral Euclidean lattices. Zbl 1236.11059 Bannai, Eiichi; Miezaki, Tsuyoshi 4 2012 Maximal \(m\)-distance sets containing the representation of the Johnson graph \(J(n,m)\). Zbl 1252.05150 Bannai, Eiichi; Sato, Takahiro; Shigezumi, Junichi 3 2012 A new Euclidean tight 6-design. Zbl 1256.05034 Bannai, Eiichi; Bannai, Etsuko; Shigezumi, Junichi 2 2012 On the existence of minimum cubature formulas for Gaussian measure on \(\mathbb R^{2}\) of degree \(t\) supported by \([\frac{t}{4}]+1\) circles. Zbl 1235.05027 Bannai, Eiichi; Bannai, Etsuko; Hirao, Masatake; Sawa, Masanori 1 2012 An elementary approach to toy models for D. H. Lehmer’s conjecture. Zbl 1293.11067 Bannai, Eiichi; Miezaki, Tsuyoshi; Yudin, Vladimir A. 5 2011 A note on anticoherent spin states. Zbl 1225.81072 Bannai, Eiichi; Tagami, Makoto 2 2011 Tight 9-designs on two concentric spheres. Zbl 1235.05026 Bannai, Eiichi; Bannai, Etsuko 2 2011 Cubature formulas in numerical analysis and Euclidean tight designs. Zbl 1227.05107 Bannai, Eiichi; Bannai, Etsuko; Hirao, Masatake; Sawa, Masanori 11 2010 Euclidean designs and coherent configurations. Zbl 1231.05019 Bannai, Eiichi; Bannai, Etsuko 11 2010 Toy models for D. H. Lehmer’s conjecture. Zbl 1216.11048 Bannai, Eiichi; Miezaki, Tsuyoshi 7 2010 A survey on spherical designs and algebraic combinatorics on spheres. Zbl 1207.05022 Bannai, Eiichi; Bannai, Etsuko 77 2009 Association schemes related to universally optimal configurations, Kerdock codes and extremal Euclidean line-sets. Zbl 1250.05119 Abdukhalikov, Kanat; Bannai, Eiichi; Suda, Sho 13 2009 On antipodal spherical \(t\)-designs of degree \(s\) with \(t\geq 2s-3\). Zbl 1270.05017 Bannai, Eiichi; Bannai, Etsuko 10 2009 Finite Euclidean graphs and Ramanujan graphs. Zbl 1208.05046 Bannai, Eiichi; Shimabukuro, Osamu; Tanaka, Hajime 9 2009 Spherical designs and Euclidean designs. Zbl 1209.05266 Bannai, Eiichi; Bannai, Etsuko 8 2009 The mathematics of Donald Gordon Higman. Zbl 1165.01309 Bannai, Eiichi; Griess, Robert L. jun.; Praeger, Cheryl E.; Scott, Leonard 3 2009 Uniqueness of certain association schemes. Zbl 1200.05258 Bannai, Eiichi; Bannai, Etsuko; Bannai, Hideo 5 2008 On the zeros of Hecke-type Faber polynomials. Zbl 1190.11030 Bannai, Eiichi; Kojima, Koji; Miezaki, Tsuyoshi 1 2008 On the strong non-rigidity of certain tight Euclidean designs. Zbl 1123.05024 Bannai, Eiichi; Bannai, Etsuko; Suprijanto, Djoko 7 2007 On Euclidean tight 4-designs. Zbl 1104.05016 Bannai, Eiichi; Bannai, Etsuko 22 2006 Spherical designs attached to extremal lattices and the modulo \(p\) property of Fourier coefficients of extremal modular forms. Zbl 1121.11046 Bannai, Eiichi; Koike, Masao; Shinohara, Masashi; Tagami, Makoto 9 2006 On primitive symmetric association schemes with \(m_1=3\). Zbl 1093.05073 Bannai, Eiichi; Bannai, Etsuko 6 2006 On optimal tight 4-designs on 2 concentric spheres. Zbl 1083.62067 Bannai, Eiichi; Bannai, Etsuko 5 2006 The nonexistence of certain tight spherical designs. Zbl 1072.05017 Bannai, E.; Munemasa, A.; Venkov, B. 31 2005 Tight Gaussian 4-designs. Zbl 1069.05016 Bannai, Eiichi; Bannai, Etsuko 9 2005 A note on the spherical embeddings of strongly regular graphs. Zbl 1071.05074 Bannai, Eiichi; Bannai, Etsuko 8 2005 Codes and designs in Grassmannian spaces. Zbl 1040.05005 Bachoc, Christine; Bannai, Eiichi; Coulangeon, Renaud 22 2004 Finite analogues of non-Euclidean spaces and Ramanujan graphs. Zbl 1033.05099 Bannai, Eiichi; Shimabukuro, Osamu; Tanaka, Hajime 13 2004 Type II codes over \(\mathbb F_2+ u\mathbb F_2\) and applications to Hermitian modular forms. Zbl 1048.11038 Bannai, Eiichi; Harada, Masaaki; Ibukiyama, Tomoyoshi; Munemasa, Akihiro; Oura, Manabu 22 2003 The decomposition of the permutation character \(1^{\text{GL}(2n,q)}_{\text{GL}(n,q^2)}\). Zbl 1031.20040 Bannai, Eiichi; Tanaka, Hajime 6 2003 Some results on modular forms – subgroups of the modular group whose ring of modular forms is a polynomial ring. Zbl 1029.11012 Bannai, Eiichi; Koike, Masao; Munemasa, Akihiro; Sekiguchi, Jiro 6 2001 Modular invariants of the modular data of finite groups. Zbl 0991.05510 Bannai, Eiichi; Bannai, Etsuko; Shimabukuro, Osamu; Tagami, Makoto 1 2001 Sphere packings, lattices and groups. With additional contributions by E. Bannai, R. E. Borcherds, J. Leech, S. P. Norton, A. M. Odlyzko, R. A. Parker, L. Queen and B. B. Venkov. 3rd ed. Zbl 0915.52003 Conway, J. H.; Sloane, N. J. A. 590 1999 Type II codes, even unimodular lattices, and invariant rings. Zbl 0958.94042 Bannai, Eiichi; Dougherty, Steven T.; Harada, Masaaki; Oura, Manabu 61 1999 An introduction to association schemes. Zbl 0967.05068 Bannai, Eiichi 4 1999 Thoughts on modular forms. Zbl 0957.11500 Bannai, Eiichi 4 1999 Modular invariance property of association schemes, type II codes over finite rings and finite abelian groups and reminiscences of François Jaeger (a survey). Zbl 0917.05086 Bannai, Eiichi 4 1999 On the ring of simultaneous invariants for the Gleason-MacWilliams group. Zbl 0944.15022 Bannai, Eiichi; Bannai, Etsuko; Ozeki, Michio; Teranishi, Yasuo 3 1999 Type II codes over \({\mathbb{F}}_2+u{\mathbb{F}}_2\) and an application to Hermitian modular forms. Zbl 0957.11501 Bannai, Eiichi; Harada, Masaaki; Munemasa, Akihiro; Oura, Manabu 1 1999 On spin models, modular invariance, and duality. Zbl 0880.05083 Bannai, Eiichi; Bannai, Etsuko; Jaeger, François 22 1997 On association schemes of balanced property with \(m_1=4\). Zbl 0935.05095 Bannai, Eiichi; Sali, Attila 1 1997 Construction of Jacobi forms from certain combinatorial polynomials. Zbl 0860.11026 Bannai, Eiichi; Ozeki, Michio 10 1996 On Jacobi forms of weight 4. Zbl 0896.11018 Bannai, Eiichi; Minashima, Shinri; Ozeki, Michio 2 1996 Progress in algebraic combinatorics. Based on the international symposium on algebraic combinatorics, Fukuoka, Japan, 1993 and the research project on algebraic combinatorics, Kyoto, Japan, April 1994 – March 1995. Zbl 0845.00006 2 1996 Generalized generalized spin models (four-weight spin models). Zbl 0848.05072 Bannai, Eiichi; Bannai, Etsuko 28 1995 The Terwilliger algebras of group association schemes. Zbl 0839.05095 Bannai, Eiichi; Munemasa, Akihiro 21 1995 Spin models on finite cyclic groups. Zbl 0803.05058 Bannai, Eiichi; Bannai, Etsuko 22 1994 Classification of small spin models. Zbl 0823.05065 Bannai, Eiichi; Jaeger, François; Sali, Attila 7 1994 Modular invariance of the character table of the Hamming association scheme \(H(d,q)\). Zbl 0799.05068 Bannai, Eiichi; Bannai, Etsuko 4 1994 Association schemes and fusion algebras. (An introduction). Zbl 0790.05098 Bannai, Eiichi 19 1993 Character tables of fission schemes and fusion schemes. Zbl 0794.05131 Bannai, Eiichi; Song, Sung Yell 15 1993 Generalized spin models and association schemes. Zbl 0797.05082 Bannai, Eiichi; Bannai, Etsuko 7 1993 Latest topics in algebraic combinatorics and association schemes. Zbl 0794.05130 Bannai, Eiichi 3 1993 On a theorem of Ikuta, Ito and Munemasa. Zbl 0753.05080 Bannai, Eiichi 1 1992 Subschemes of some association schemes. Zbl 0762.20004 Bannai, Eiichi 42 1991 Character tables of certain association schemes coming from finite unitary and symplectic groups. Zbl 0824.20009 Bannai, Eiichi; Song, Sung-Yell; Hao, Shen; Wei, Hongzeng 6 1991 Character tables of the association schemes of finite orthogonal groups acting on the nonisotropic points. Zbl 0762.20005 Bannai, Eiichi; Hao, Shen; Song, Sung-Yell 20 1990 The character table of the Hecke algebra \({\mathcal H}(GL_{2n}(\mathbb{F}_ q),Sp_{2n}(\mathbb{F}_ q))\). Zbl 0761.20013 Bannai, Eiichi; Kawanaka, Noriaki; Song, Sung-Yell 16 1990 Character tables of commutative association schemes. Zbl 0757.05100 Bannai, Eiichi 14 1990 Orthogonal polynomials in coding theory and algebraic combinatorics. Zbl 0704.42025 Bannai, Eiichi 6 1990 The character table of the commutative association scheme coming from the action of \(GL(n,q)\) on non-incident point-hyperplane pairs. Zbl 0762.20003 Bannai, Eiichi; Song, Sung-Yell 4 1990 Ennola type dualities in the character tables of some association schemes. Zbl 0808.20011 Bannai, Eiichi; Kwok, Wing Man; Song, Sung Yell 2 1990 On distance-regular graphs with fixed valency. IV. Zbl 0677.05061 Bannai, Eiichi; Ito, Tatsuro 12 1989 Tight t-designs and squarefree integers. Zbl 0713.05009 Bannai, E.; Hoggar, S. G. 10 1989 The character tables of Paige’s simple Moufang loops and their relationship to the character tables of PSL(2,q). Zbl 0682.20050 Bannai, Eiichi; Song, Sung-Yell 9 1989 On the number of elements which are not \(n\)-th powers in finite groups. Zbl 0684.20016 Bannai, E.; Deza, M.; Frankl, P.; Kim, A. C.; Kiyota, M. 2 1989 On the character table of the association scheme \(Sp(4,q)/Sz(q)\). Zbl 0762.20002 Bannai, Eiichi; Song, Sung-Yell 1 1989 Sphere packings, lattices and groups. With additional contributions by E. Bannai, J. Leech, S. P. Norton, A. M. Odlyzko, R. A. Parker, L. Queen and B. B. Venkov. Zbl 0634.52002 Conway, J. H.; Sloane, N. J. A. 418 1988 On distance-regular graphs with fixed valency. II. Zbl 0699.05038 Bannai, Eiichi; Ito, Tatsuro 14 1988 On extremal finite sets in the sphere and other metric spaces. Zbl 0723.05113 Bannai, E. 14 1988 On distance-regular graphs with fixed valency. Zbl 0626.05050 Bannai, Eiichi; Ito, Tatsuro 16 1987 On distance-regular graphs with fixed valency. III. Zbl 0677.05060 Bannai, Eiichi; Ito, Tatsuro 11 1987 The study of distance-regular graphs from the algebraic (i.e., character theoretical) viewpoint. Zbl 0677.05059 Bannai, Eiichi; Ito, Tatsuro 6 1987 Rigid spherical t-designs and a theorem of Y. Hong. Zbl 0718.05016 Bannai, Eiichi 6 1987 ...and 47 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 1,201 Authors 70 Bannai, Eiichi 63 Terwilliger, Paul M. 37 Vinet, Luc 32 Bannai, Etsuko 30 Nomura, Kazumasa 29 Muzychuk, Mikhail E. 29 Suda, Sho 28 Koolen, Jack H. 28 Wang, Kaishun 28 Xu, Bangteng 24 Ito, Tatsuro 24 Munemasa, Akihiro 23 Nozaki, Hiroshi 22 Hirasaka, Mitsugu 22 Tanaka, Hajime 21 Gao, Suogang 21 Guo, Jun 21 Zhedanov, Alexei S. 20 Hanaki, Akihide 20 Ponomarenko, Ilya Nikolaevich 20 Solé, Patrick 19 Hiraki, Akira 17 Miezaki, Tsuyoshi 17 Miklavič, Štefko 16 Suzuki, Hiroshi 16 Zhu, Yan 15 MacLean, Mark S. 14 Curtin, Brian 14 Hou, Bo 14 Li, Fenggao 14 Song, Sung-Yell 13 Kharaghani, Hadi 13 Sawa, Masanori 13 Yu, Wei-Hsuan 12 Blau, Harvey I. 12 Boĭvalenkov, Pet”r Georgiev 12 Crampé, Nicolas 11 Dinh, Hai Quang 11 Dougherty, Steven T. 11 Harada, Masaaki 11 Ivanov, Alexander A. 11 Ma, Jianmin 11 Martin, William J. 11 Miller, Mirka 10 Hirao, Masatake 10 Ikuta, Takuya 10 Klin, Mikhail H. 10 Praeger, Cheryl Elisabeth 10 Smith, Jonathan Dallas Hayden 10 Weng, Chih-Wen 9 Balbuena, Camino 9 Oura, Manabu 9 Tsujimoto, Satoshi 8 Choie, YoungJu 8 Evdokimov, Sergeĭ Alekseevich 8 Gavrilyuk, Alexander L. 8 Genest, Vincent X. 8 Godsil, Christopher David 8 Gräf, Manuel 8 Johnson, Kenneth W. 8 Lee, Jaeho 8 Momihara, Koji 8 Okuda, Takayuki 8 Shimabukuro, Osamu 8 Zhao, Da 7 Arad, Zvi 7 Araujo-Pardo, Gabriela 7 Bachoc, Christine 7 Bamberg, John 7 Bang, Sejeong 7 Caughman, John S. IV 7 Ehler, Martin 7 Feng, Tao 7 Fiol, Miquel Angel 7 Mixon, Dustin G. 7 Penjic, Safet 7 Shinohara, Masashi 7 Van Dam, Edwin Robert 7 Wang, Yangxian 7 Zuber, Jean-Bernard 6 Ankur, Raghav 6 Bernard, Pierre-Antoine 6 Cameron, Peter Jephson 6 Cioabă, Sebastian M. 6 Herman, Allen 6 Jasper, John Sahayam 6 Kurihara, Hirotake 6 Lee, Yoonjin 6 Lv, Benjian 6 Moulton, Vincent L. 6 Pascasio, Arlene A. 6 Pasechnik, Dmitrii V. 6 Sriboonchitta, Songsak 6 Stanton, Dennis W. 6 Stoyanova, Maya M. 6 Tan, Yingying 6 Woldar, Andrew J. 6 Yang, Yuefeng 5 Brouwer, Andries Evert 5 Gao, You ...and 1,101 more Authors all top 5 Cited in 223 Serials 151 European Journal of Combinatorics 122 Discrete Mathematics 106 Journal of Algebraic Combinatorics 98 Linear Algebra and its Applications 88 Journal of Combinatorial Theory. Series A 71 Graphs and Combinatorics 67 Journal of Algebra 54 Designs, Codes and Cryptography 42 Journal of Combinatorial Theory. 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Series A 2 Chinese Science Bulletin 2 SIAM Journal on Optimization ...and 123 more Serials all top 5 Cited in 54 Fields 1,096 Combinatorics (05-XX) 260 Group theory and generalizations (20-XX) 190 Information and communication theory, circuits (94-XX) 124 Number theory (11-XX) 107 Special functions (33-XX) 95 Geometry (51-XX) 94 Linear and multilinear algebra; matrix theory (15-XX) 67 Quantum theory (81-XX) 60 Associative rings and algebras (16-XX) 56 Nonassociative rings and algebras (17-XX) 52 Convex and discrete geometry (52-XX) 48 Numerical analysis (65-XX) 45 Harmonic analysis on Euclidean spaces (42-XX) 39 Operations research, mathematical programming (90-XX) 32 Computer science (68-XX) 27 Approximations and expansions (41-XX) 24 Statistics (62-XX) 22 Commutative algebra (13-XX) 21 Abstract harmonic analysis (43-XX) 20 Algebraic geometry (14-XX) 19 Probability theory and stochastic processes (60-XX) 16 Functional analysis (46-XX) 16 Statistical mechanics, structure of matter (82-XX) 13 Order, lattices, ordered algebraic structures (06-XX) 13 Topological groups, Lie groups (22-XX) 12 Field theory and polynomials (12-XX) 12 Manifolds and cell complexes (57-XX) 7 Partial differential equations (35-XX) 6 Category theory; homological algebra (18-XX) 6 Operator theory (47-XX) 5 History and biography (01-XX) 5 Mathematical logic and foundations (03-XX) 4 Potential theory (31-XX) 4 Dynamical systems and ergodic theory (37-XX) 4 Differential geometry (53-XX) 3 \(K\)-theory (19-XX) 3 Several complex variables and analytic spaces (32-XX) 3 Difference and functional equations (39-XX) 3 Global analysis, analysis on manifolds (58-XX) 3 Mechanics of particles and systems (70-XX) 3 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 2 General and overarching topics; collections (00-XX) 2 Real functions (26-XX) 2 Ordinary differential equations (34-XX) 2 Integral transforms, operational calculus (44-XX) 2 Mechanics of deformable solids (74-XX) 2 Biology and other natural sciences (92-XX) 1 General algebraic systems (08-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 General topology (54-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Relativity and gravitational theory (83-XX) 1 Systems theory; control (93-XX) 1 Mathematics education (97-XX) Citations by Year