Bannai, Eiichi; Bannai, Etsuko; Tanaka, Hajime; Zhu, Yan Tight relative \(t\)-designs on two shells in hypercubes, and Hahn and Hermite polynomials. (English) Zbl 07523680 Ars Math. Contemp. 22, No. 2, Paper No. 1, 43 p. (2022). MSC: 05B30 05E30 33C45 PDF BibTeX XML Cite \textit{E. Bannai} et al., Ars Math. Contemp. 22, No. 2, Paper No. 1, 43 p. (2022; Zbl 07523680) Full Text: DOI OpenURL
Hou, Lihang; Hou, Bo; Kang, Na; Gao, Suogang The Terwilliger algebra of the halved \(n\)-cube from the viewpoint of its automorphism group action. (English) Zbl 1480.05144 Eur. J. Comb. 101, Article ID 103480, 15 p. (2022). MSC: 05E30 05E18 PDF BibTeX XML Cite \textit{L. Hou} et al., Eur. J. Comb. 101, Article ID 103480, 15 p. (2022; Zbl 1480.05144) Full Text: DOI OpenURL
Liang, Xiaoye; Tan, Ying-Ying; Koolen, Jack Thin distance-regular graphs with classical parameters \((D, q, q, \frac{q^t-1}{q-1}-1)\) with \(t> D\) are the Grassmann graphs. (English) Zbl 07503016 Electron. J. Comb. 28, No. 4, Research Paper P4.45, 21 p. (2021). MSC: 05C50 05C12 05C75 05E30 PDF BibTeX XML Cite \textit{X. Liang} et al., Electron. J. Comb. 28, No. 4, Research Paper P4.45, 21 p. (2021; Zbl 07503016) Full Text: DOI OpenURL
Morales, John Vincent S.; Palma, Tessie M. On quantum adjacency algebras of Doob graphs and their irreducible modules. (English) Zbl 1479.05369 J. Algebr. Comb. 54, No. 4, 979-998 (2021). MSC: 05E30 05C50 81S25 15A04 PDF BibTeX XML Cite \textit{J. V. S. Morales} and \textit{T. M. Palma}, J. Algebr. Comb. 54, No. 4, 979--998 (2021; Zbl 1479.05369) Full Text: DOI OpenURL
Xu, Jing; Ito, Tatsuro; Li, Shuang-Dong Irreducible representations of the Terwilliger algebra of a tree. (English) Zbl 07433378 Graphs Comb. 37, No. 5, 1749-1773 (2021). MSC: 05E10 05E16 05E30 20C08 PDF BibTeX XML Cite \textit{J. Xu} et al., Graphs Comb. 37, No. 5, 1749--1773 (2021; Zbl 07433378) Full Text: DOI OpenURL
Hanaki, Akihide Modular Terwilliger algebras of association schemes. (English) Zbl 1479.05366 Graphs Comb. 37, No. 5, 1521-1529 (2021). MSC: 05E30 PDF BibTeX XML Cite \textit{A. Hanaki}, Graphs Comb. 37, No. 5, 1521--1529 (2021; Zbl 1479.05366) Full Text: DOI arXiv OpenURL
Brosch, D.; Laurent, M.; Steenkamp, A. Optimizing hypergraph-based polynomials modeling job-occupancy in queuing with redundancy scheduling. (English) Zbl 1477.90056 SIAM J. Optim. 31, No. 3, 2227-2254 (2021). MSC: 90C23 90C26 90B22 PDF BibTeX XML Cite \textit{D. Brosch} et al., SIAM J. Optim. 31, No. 3, 2227--2254 (2021; Zbl 1477.90056) Full Text: DOI arXiv OpenURL
Fernández, Blas; Miklavič, Štefko On bipartite graphs with exactly one irreducible \(T\)-module with endpoint 1, which is thin. (English) Zbl 1469.05165 Eur. J. Comb. 97, Article ID 103387, 15 p. (2021). MSC: 05E30 05E16 05C12 PDF BibTeX XML Cite \textit{B. Fernández} and \textit{Š. Miklavič}, Eur. J. Comb. 97, Article ID 103387, 15 p. (2021; Zbl 1469.05165) Full Text: DOI OpenURL
MacLean, Mark S.; Penjić, Safet A combinatorial basis for Terwilliger algebra modules of a bipartite distance-regular graph. (English) Zbl 1466.05226 Discrete Math. 344, No. 7, Article ID 112393, 17 p. (2021). MSC: 05E30 05C12 33C80 PDF BibTeX XML Cite \textit{M. S. MacLean} and \textit{S. Penjić}, Discrete Math. 344, No. 7, Article ID 112393, 17 p. (2021; Zbl 1466.05226) Full Text: DOI OpenURL
Martin, William J. Scaffolds: a graph-theoretic tool for tensor computations related to Bose-Mesner algebras. (English) Zbl 1462.05362 Linear Algebra Appl. 619, 50-106 (2021). MSC: 05E30 15A72 16S50 05C83 05C90 PDF BibTeX XML Cite \textit{W. J. Martin}, Linear Algebra Appl. 619, 50--106 (2021; Zbl 1462.05362) Full Text: DOI OpenURL
Li, Shuang-Dong; Fan, Yi-Zheng; Ito, Tatsuro; Karimi, Masoud; Xu, Jing The isomorphism problem of trees from the viewpoint of Terwilliger algebras. (English) Zbl 1448.05234 J. Comb. Theory, Ser. A 177, Article ID 105328, 11 p. (2021). MSC: 05E30 05C60 05C05 PDF BibTeX XML Cite \textit{S.-D. Li} et al., J. Comb. Theory, Ser. A 177, Article ID 105328, 11 p. (2021; Zbl 1448.05234) Full Text: DOI arXiv OpenURL
Maclean, Mark S.; Miklavič, Štefko On a certain class of 1-thin distance-regular graphs. (English) Zbl 1464.05360 Ars Math. Contemp. 18, No. 2, 187-210 (2020). MSC: 05E30 PDF BibTeX XML Cite \textit{M. S. Maclean} and \textit{Š. Miklavič}, Ars Math. Contemp. 18, No. 2, 187--210 (2020; Zbl 1464.05360) Full Text: DOI OpenURL
Miklavič, Štefko; Penjić, Safet On the Terwilliger algebra of certain family of bipartite distance-regular graphs with \(\Delta_2 = 0\). (English) Zbl 1441.05248 Art Discrete Appl. Math. 3, No. 2, Paper No. P2.04, 14 p. (2020). MSC: 05E30 05C50 PDF BibTeX XML Cite \textit{Š. Miklavič} and \textit{S. Penjić}, Art Discrete Appl. Math. 3, No. 2, Paper No. P2.04, 14 p. (2020; Zbl 1441.05248) Full Text: DOI OpenURL
Lee, Jae-Ho Grassmann graphs, degenerate DAHA, and non-symmetric dual \(q\)-Hahn polynomials. (English) Zbl 1437.05241 Linear Algebra Appl. 588, 160-195 (2020). MSC: 05E30 20C08 33D45 33D80 PDF BibTeX XML Cite \textit{J.-H. Lee}, Linear Algebra Appl. 588, 160--195 (2020; Zbl 1437.05241) Full Text: DOI arXiv OpenURL
Fernández, Blas; Miklavič, Štefko On the Terwilliger algebra of distance-biregular graphs. (English) Zbl 1448.05099 Linear Algebra Appl. 597, 18-32 (2020). Reviewer: Vilmar Trevisan (Porto Alegre) MSC: 05C25 PDF BibTeX XML Cite \textit{B. Fernández} and \textit{Š. Miklavič}, Linear Algebra Appl. 597, 18--32 (2020; Zbl 1448.05099) Full Text: DOI OpenURL
Liang, Xiaoye; Ito, Tatsuro; Watanabe, Yuta The Terwilliger algebra of the Grassmann scheme \(J_q(N,D)\) revisited from the viewpoint of the quantum affine algebra \(U_q(\hat{\mathfrak{sl}}_2)\). (English) Zbl 1435.05239 Linear Algebra Appl. 596, 117-144 (2020). MSC: 05E30 05E10 20G42 33C80 14M15 PDF BibTeX XML Cite \textit{X. Liang} et al., Linear Algebra Appl. 596, 117--144 (2020; Zbl 1435.05239) Full Text: DOI OpenURL
Hou, Lihang; Hou, Bo; Gao, Suogang; Yu, Wei-Hsuan New code upper bounds for the folded \(n\)-cube. (English) Zbl 1433.05333 J. Comb. Theory, Ser. A 172, Article ID 105182, 27 p. (2020). MSC: 05E30 05C12 94B65 94B05 90C22 PDF BibTeX XML Cite \textit{L. Hou} et al., J. Comb. Theory, Ser. A 172, Article ID 105182, 27 p. (2020; Zbl 1433.05333) Full Text: DOI arXiv OpenURL
Sumalroj, Supalak A diagram associated with the subconstituent algebra of a distance-regular graph. (English) Zbl 1433.05338 Ars Math. Contemp. 17, No. 1, 185-202 (2019). MSC: 05E30 05C12 PDF BibTeX XML Cite \textit{S. Sumalroj}, Ars Math. Contemp. 17, No. 1, 185--202 (2019; Zbl 1433.05338) Full Text: DOI arXiv OpenURL
Tan, Ying-Ying; Fan, Yi-Zheng; Ito, Tatsuro; Liang, Xiaoye The Terwilliger algebra of the Johnson scheme \(J(N, D)\) revisited from the viewpoint of group representations. (English) Zbl 1415.05181 Eur. J. Comb. 80, 157-171 (2019). MSC: 05E10 05E30 05E18 PDF BibTeX XML Cite \textit{Y.-Y. Tan} et al., Eur. J. Comb. 80, 157--171 (2019; Zbl 1415.05181) Full Text: DOI OpenURL
Terwilliger, Paul; Žitnik, Arjana The quantum adjacency algebra and subconstituent algebra of a graph. (English) Zbl 1416.05142 J. Comb. Theory, Ser. A 166, 297-314 (2019). MSC: 05C25 81S25 PDF BibTeX XML Cite \textit{P. Terwilliger} and \textit{A. Žitnik}, J. Comb. Theory, Ser. A 166, 297--314 (2019; Zbl 1416.05142) Full Text: DOI arXiv OpenURL
Hamid, Nur; Oura, Manabu Terwilliger algebras of some group association schemes. (English) Zbl 1414.05314 Math. J. Okayama Univ. 61, 199-204 (2019). Reviewer: Dragan Stevanović (Niš) MSC: 05E30 PDF BibTeX XML Cite \textit{N. Hamid} and \textit{M. Oura}, Math. J. Okayama Univ. 61, 199--204 (2019; Zbl 1414.05314) OpenURL
MacLean, Mark S.; Miklavič, Štefko; Penjić, Safet An \(A\)-invariant subspace for bipartite distance-regular graphs with exactly two irreducible \(T\)-modules with endpoint 2, both thin. (English) Zbl 1404.05042 J. Algebr. Comb. 48, No. 3, 511-548 (2018). MSC: 05C12 PDF BibTeX XML Cite \textit{M. S. MacLean} et al., J. Algebr. Comb. 48, No. 3, 511--548 (2018; Zbl 1404.05042) Full Text: DOI OpenURL
Suzuki, Hiroshi Distance-regular graphs of large diameter that are completely regular clique graphs. (English) Zbl 1401.05319 J. Algebr. Comb. 48, No. 3, 369-404 (2018). MSC: 05E30 05C12 05C40 PDF BibTeX XML Cite \textit{H. Suzuki}, J. Algebr. Comb. 48, No. 3, 369--404 (2018; Zbl 1401.05319) Full Text: DOI OpenURL
Tomiyama, Masato The Terwilliger algebra of the incidence graph of the Hamming graph. (English) Zbl 1396.05050 J. Algebr. Comb. 48, No. 1, 77-118 (2018). MSC: 05C25 05C12 05E30 PDF BibTeX XML Cite \textit{M. Tomiyama}, J. Algebr. Comb. 48, No. 1, 77--118 (2018; Zbl 1396.05050) Full Text: DOI OpenURL
Morales, John Vincent S.; Tanaka, Hajime An Assmus-Mattson theorem for codes over commutative association schemes. (English) Zbl 1384.05184 Des. Codes Cryptography 86, No. 5, 1039-1062 (2018). MSC: 05E30 94B05 05B05 PDF BibTeX XML Cite \textit{J. V. S. Morales} and \textit{H. Tanaka}, Des. Codes Cryptography 86, No. 5, 1039--1062 (2018; Zbl 1384.05184) Full Text: DOI arXiv OpenURL
Jafarizadeh, M. A.; Eghbalifam, F.; Nami, S. Entanglement entropy in the spinless free fermion model and its application to the graph isomorphism problem. (English) Zbl 1397.81040 J. Phys. A, Math. Theor. 51, No. 7, Article ID 075304, 37 p. (2018). Reviewer: Hichem Eleuch (College Station) MSC: 81P40 05C60 PDF BibTeX XML Cite \textit{M. A. Jafarizadeh} et al., J. Phys. A, Math. Theor. 51, No. 7, Article ID 075304, 37 p. (2018; Zbl 1397.81040) Full Text: DOI OpenURL
Lee, Jae-Ho; Tanaka, Hajime Dual polar graphs, a nil-DAHA of rank one, and non-symmetric dual \(q\)-Krawtchouk polynomials. (English) Zbl 1381.05092 SIGMA, Symmetry Integrability Geom. Methods Appl. 14, Paper 009, 27 p. (2018). MSC: 05E30 20C08 33D45 33D80 PDF BibTeX XML Cite \textit{J.-H. Lee} and \textit{H. Tanaka}, SIGMA, Symmetry Integrability Geom. Methods Appl. 14, Paper 009, 27 p. (2018; Zbl 1381.05092) Full Text: DOI OpenURL
Lee, Jae-Ho; Tanaka, Hajime Dual polar graphs, a nil-DAHA of rank one, and non-symmetric dual \(q\)-Krawtchouk polynomials. (English) Zbl 1384.05079 Sémin. Lothar. Comb. 78B, 78B.42, 12 p. (2017). MSC: 05C12 05C69 05C31 PDF BibTeX XML Cite \textit{J.-H. Lee} and \textit{H. Tanaka}, Sémin. Lothar. Comb. 78B, 78B.42, 12 p. (2017; Zbl 1384.05079) Full Text: arXiv Link OpenURL
Lv, Benjian Terwilliger algebra for a family of folded cube graphs. (Chinese. English summary) Zbl 1389.05101 J. Beijing Norm. Univ., Nat. Sci. 53, No. 2, 137-139 (2017). MSC: 05C50 05C75 PDF BibTeX XML Cite \textit{B. Lv}, J. Beijing Norm. Univ., Nat. Sci. 53, No. 2, 137--139 (2017; Zbl 1389.05101) Full Text: DOI OpenURL
Liang, Xiaoye; Tan, Ying-Ying; Ito, Tatsuro An observation on Leonard system parameters for the Terwilliger algebra of the Johnson scheme \(J(N, D)\). (English) Zbl 1372.05234 Graphs Comb. 33, No. 1, 149-156 (2017). MSC: 05E30 05E18 33C80 PDF BibTeX XML Cite \textit{X. Liang} et al., Graphs Comb. 33, No. 1, 149--156 (2017; Zbl 1372.05234) Full Text: DOI OpenURL
Bannai, Eiichi; Bannai, Etsuko; Tanaka, Hajime; Zhu, Yan Design theory from the viewpoint of algebraic combinatorics. (English) Zbl 1365.05301 Graphs Comb. 33, No. 1, 1-41 (2017). MSC: 05E30 05B99 PDF BibTeX XML Cite \textit{E. Bannai} et al., Graphs Comb. 33, No. 1, 1--41 (2017; Zbl 1365.05301) Full Text: DOI OpenURL
MacLean, Mark S.; Miklavič, Štefko On bipartite distance-regular graphs with exactly one non-thin \(T\)-module with endpoint two. (English) Zbl 1365.05078 Eur. J. Comb. 64, 125-137 (2017). MSC: 05C12 PDF BibTeX XML Cite \textit{M. S. MacLean} and \textit{Š. Miklavič}, Eur. J. Comb. 64, 125--137 (2017; Zbl 1365.05078) Full Text: DOI OpenURL
Song, Sung Y.; Xu, Bangteng; Zhou, Shenglin Combinatorial extensions of Terwilliger algebras and wreath products of association schemes. (English) Zbl 1357.05148 Discrete Math. 340, No. 5, 892-905 (2017). MSC: 05E30 05E15 PDF BibTeX XML Cite \textit{S. Y. Song} et al., Discrete Math. 340, No. 5, 892--905 (2017; Zbl 1357.05148) Full Text: DOI OpenURL
MacLean, Mark S.; Miklavič, Štefko On bipartite distance-regular graphs with exactly two irreducible T-modules with endpoint two. (English) Zbl 1352.05196 Linear Algebra Appl. 515, 275-297 (2017). MSC: 05E30 05C12 PDF BibTeX XML Cite \textit{M. S. MacLean} and \textit{Š. Miklavič}, Linear Algebra Appl. 515, 275--297 (2017; Zbl 1352.05196) Full Text: DOI arXiv OpenURL
Penjić, Safet On the Terwilliger algebra of bipartite distance-regular graphs with \(\Delta_2 = 0\) and \(c_2 = 2\). (English) Zbl 1351.05066 Discrete Math. 340, No. 3, 452-466 (2017). MSC: 05C12 05C25 05E30 PDF BibTeX XML Cite \textit{S. Penjić}, Discrete Math. 340, No. 3, 452--466 (2017; Zbl 1351.05066) Full Text: DOI OpenURL
Morales, John Vincent S. On Lee association schemes over \(\mathbb{Z}_4\) and their Terwilliger algebra. (English) Zbl 1352.05197 Linear Algebra Appl. 510, 311-328 (2016). MSC: 05E30 05C50 15A04 20C30 33C45 PDF BibTeX XML Cite \textit{J. V. S. Morales}, Linear Algebra Appl. 510, 311--328 (2016; Zbl 1352.05197) Full Text: DOI OpenURL
Kim, Kijung Terwilliger algebras of wreath products by 3-equivalenced schemes. (English) Zbl 1337.05115 Commun. Algebra 44, No. 3, 1131-1142 (2016). MSC: 05E15 05E30 PDF BibTeX XML Cite \textit{K. Kim}, Commun. Algebra 44, No. 3, 1131--1142 (2016; Zbl 1337.05115) Full Text: DOI arXiv OpenURL
Suzuki, Hiroshi Completely regular clique graphs. II. (English) Zbl 1331.05173 J. Algebr. Comb. 43, No. 2, 417-445 (2016). MSC: 05C69 05C40 05C30 05C12 PDF BibTeX XML Cite \textit{H. Suzuki}, J. Algebr. Comb. 43, No. 2, 417--445 (2016; Zbl 1331.05173) Full Text: DOI OpenURL
MacLean, Mark S.; Miklavič, Štefko; Penjić, Safet On the Terwilliger algebra of bipartite distance-regular graphs with \(\Delta_{2}=0\) and \(c_{2}=1\). (English) Zbl 1331.05237 Linear Algebra Appl. 496, 307-330 (2016). MSC: 05E30 05C50 05C12 PDF BibTeX XML Cite \textit{M. S. MacLean} et al., Linear Algebra Appl. 496, 307--330 (2016; Zbl 1331.05237) Full Text: DOI OpenURL
Bannai, Eiichi; Bannai, Etsuko; Suda, Sho; Tanaka, Hajime On relative \(t\)-designs in polynomial association schemes. (English) Zbl 1329.05307 Electron. J. Comb. 22, No. 4, Research Paper P4.47, 17 p. (2015). MSC: 05E30 05B30 PDF BibTeX XML Cite \textit{E. Bannai} et al., Electron. J. Comb. 22, No. 4, Research Paper P4.47, 17 p. (2015; Zbl 1329.05307) Full Text: arXiv Link OpenURL
Liu, Huan; Hou, Bo; Gao, Suogang Leonard triples, the Racah algebra, and some distance-regular graphs of Racah type. (English) Zbl 1325.05185 Linear Algebra Appl. 484, 435-456 (2015). MSC: 05E30 05C12 15A04 33D45 PDF BibTeX XML Cite \textit{H. Liu} et al., Linear Algebra Appl. 484, 435--456 (2015; Zbl 1325.05185) Full Text: DOI OpenURL
Lv, Benjian; Wang, Kaishun The Terwilliger algebra of the incidence graphs of Johnson geometry. II. (English) Zbl 1318.05092 Discrete Math. 338, No. 12, 2378-2386 (2015). MSC: 05E30 PDF BibTeX XML Cite \textit{B. Lv} and \textit{K. Wang}, Discrete Math. 338, No. 12, 2378--2386 (2015; Zbl 1318.05092) Full Text: DOI OpenURL
Gao, Xiaojuan; Gao, Suogang; Hou, Bo The Terwilliger algebras of Grassmann graphs. (English) Zbl 1307.05233 Linear Algebra Appl. 471, 427-448 (2015). MSC: 05E30 17B37 PDF BibTeX XML Cite \textit{X. Gao} et al., Linear Algebra Appl. 471, 427--448 (2015; Zbl 1307.05233) Full Text: DOI OpenURL
MacLean, Mark S. The local eigenvalues of a bipartite distance-regular graph. (English) Zbl 1304.05095 Eur. J. Comb. 45, 115-123 (2015). MSC: 05C50 PDF BibTeX XML Cite \textit{M. S. MacLean}, Eur. J. Comb. 45, 115--123 (2015; Zbl 1304.05095) Full Text: DOI OpenURL
Gavrilyuk, Alexander L.; Koolen, Jack H. The Terwilliger polynomial of a \(Q\)-polynomial distance-regular graph and its application to pseudo-partition graphs. (English) Zbl 1303.05214 Linear Algebra Appl. 466, 117-140 (2015). MSC: 05E30 05C31 05C12 PDF BibTeX XML Cite \textit{A. L. Gavrilyuk} and \textit{J. H. Koolen}, Linear Algebra Appl. 466, 117--140 (2015; Zbl 1303.05214) Full Text: DOI arXiv OpenURL
Ito, Tatsuro; Sato, Jugo TD-pairs of type II with shape \(1,2,\dots,2,1\). (English) Zbl 1311.15017 Linear Algebra Appl. 461, 51-91 (2014). MSC: 15A30 05E30 33C45 20G05 PDF BibTeX XML Cite \textit{T. Ito} and \textit{J. Sato}, Linear Algebra Appl. 461, 51--91 (2014; Zbl 1311.15017) Full Text: DOI OpenURL
Suzuki, Hiroshi Completely regular clique graphs. (English) Zbl 1297.05268 J. Algebr. Comb. 40, No. 1, 233-244 (2014). MSC: 05E30 05C12 05C40 05C69 PDF BibTeX XML Cite \textit{H. Suzuki}, J. Algebr. Comb. 40, No. 1, 233--244 (2014; Zbl 1297.05268) Full Text: DOI OpenURL
Lang, Michael S. Bipartite distance-regular graphs: the \(Q\)-polynomial property and pseudo primitive idempotents. (English) Zbl 1297.05264 Discrete Math. 331, 27-35 (2014). MSC: 05E30 PDF BibTeX XML Cite \textit{M. S. Lang}, Discrete Math. 331, 27--35 (2014; Zbl 1297.05264) Full Text: DOI OpenURL
Lv, Benjian; Maldonado, Carolina; Wang, Kaishun More on the Terwilliger algebra of Johnson schemes. (English) Zbl 1288.05297 Discrete Math. 328, 54-62 (2014). MSC: 05E30 PDF BibTeX XML Cite \textit{B. Lv} et al., Discrete Math. 328, 54--62 (2014; Zbl 1288.05297) Full Text: DOI arXiv OpenURL
Bogaerts, Mathieu; Dukes, Peter Semidefinite programming for permutation codes. (English) Zbl 1332.94107 Discrete Math. 326, 34-43 (2014). MSC: 94B25 05E10 90C22 PDF BibTeX XML Cite \textit{M. Bogaerts} and \textit{P. Dukes}, Discrete Math. 326, 34--43 (2014; Zbl 1332.94107) Full Text: DOI arXiv OpenURL
Gao, Suogang; Zhang, Liwei; Hou, Bo The Terwilliger algebras of Johnson graphs. (English) Zbl 1282.05217 Linear Algebra Appl. 443, 164-183 (2014). MSC: 05E30 33D80 17B37 PDF BibTeX XML Cite \textit{S. Gao} et al., Linear Algebra Appl. 443, 164--183 (2014; Zbl 1282.05217) Full Text: DOI OpenURL
Kong, Qian; Lv, Benjian; Wang, Kaishun The Terwilliger algebra of the incidence graphs of Johnson geometry. (English) Zbl 1295.05274 Electron. J. Comb. 20, No. 4, Research Paper P5, 11 p. (2013). MSC: 05E30 PDF BibTeX XML Cite \textit{Q. Kong} et al., Electron. J. Comb. 20, No. 4, Research Paper P5, 11 p. (2013; Zbl 1295.05274) Full Text: arXiv Link OpenURL
Kong, Qian; Lv, Benjian; Wang, Kaishun The Terwilliger algebra of Odd graphs. (English) Zbl 1259.05192 Discrete Math. 313, No. 5, 698-703 (2013). MSC: 05E30 PDF BibTeX XML Cite \textit{Q. Kong} et al., Discrete Math. 313, No. 5, 698--703 (2013; Zbl 1259.05192) Full Text: DOI arXiv OpenURL
Kim, Kijung Terwilliger algebras of wreath products by quasi-thin schemes. (English) Zbl 1253.05147 Linear Algebra Appl. 437, No. 11, 2773-2780 (2012). MSC: 05E15 05E30 PDF BibTeX XML Cite \textit{K. Kim}, Linear Algebra Appl. 437, No. 11, 2773--2780 (2012; Zbl 1253.05147) Full Text: DOI arXiv OpenURL
Hanaki, Akihide; Kim, Kijung; Maekawa, Yu Terwilliger algebras of direct and wreath products of association schemes. (English) Zbl 1235.05157 J. Algebra 343, No. 1, 195-200 (2011). MSC: 05E30 PDF BibTeX XML Cite \textit{A. Hanaki} et al., J. Algebra 343, No. 1, 195--200 (2011; Zbl 1235.05157) Full Text: DOI Link OpenURL
Srinivasan, Murali K. Symmetric chains, Gelfand–Tsetlin chains, and the Terwilliger algebra of the binary Hamming scheme. (English) Zbl 1229.05298 J. Algebr. Comb. 34, No. 2, 301-322 (2011). MSC: 05E30 PDF BibTeX XML Cite \textit{M. K. Srinivasan}, J. Algebr. Comb. 34, No. 2, 301--322 (2011; Zbl 1229.05298) Full Text: DOI arXiv OpenURL
Tanaka, Rie Classification of commutative association schemes with almost commutative Terwilliger algebras. (English) Zbl 1225.05258 J. Algebr. Comb. 33, No. 1, 1-10 (2011). MSC: 05E30 PDF BibTeX XML Cite \textit{R. Tanaka}, J. Algebr. Comb. 33, No. 1, 1--10 (2011; Zbl 1225.05258) Full Text: DOI OpenURL
Levstein, Fernando; Maldonado, Carolina Generalized quadrangles and subconstituent algebra. (English) Zbl 1206.05104 Cubo 12, No. 2, 53-75 (2010). MSC: 05E30 PDF BibTeX XML Cite \textit{F. Levstein} and \textit{C. Maldonado}, Cubo 12, No. 2, 53--75 (2010; Zbl 1206.05104) Full Text: DOI OpenURL
Cerzo, Diana R. Structure of thin irreducible modules of a \(Q\)-polynomial distance-regular graph. (English) Zbl 1226.05265 Linear Algebra Appl. 433, No. 8-10, 1573-1613 (2010). MSC: 05E30 05C12 PDF BibTeX XML Cite \textit{D. R. Cerzo}, Linear Algebra Appl. 433, No. 8--10, 1573--1613 (2010; Zbl 1226.05265) Full Text: DOI arXiv OpenURL
Ito, Tatsuro; Terwilliger, Paul The augmented tridiagonal algebra. (English) Zbl 1236.17022 Kyushu J. Math. 64, No. 1, 81-144 (2010). Reviewer: Alberto Elduque (Zaragoza) MSC: 17B37 05E30 33D45 PDF BibTeX XML Cite \textit{T. Ito} and \textit{P. Terwilliger}, Kyushu J. Math. 64, No. 1, 81--144 (2010; Zbl 1236.17022) Full Text: DOI arXiv OpenURL
Bhattacharyya, Gargi; Song, Sung Y.; Tanaka, Rie Terwilliger algebras of wreath products of one-class association schemes. (English) Zbl 1286.05182 J. Algebr. Comb. 31, No. 3, 455-466 (2010). MSC: 05E30 PDF BibTeX XML Cite \textit{G. Bhattacharyya} et al., J. Algebr. Comb. 31, No. 3, 455--466 (2010; Zbl 1286.05182) Full Text: DOI arXiv OpenURL
Gavrilyuk, A. L.; Makhnev, A. A. On distance-regular graphs in which the neighborhood of each vertex is isomorphic to the Hoffman-Singleton graph. (English. Russian original) Zbl 1285.05153 Dokl. Math. 80, No. 2, 665-668 (2009); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 428, No. 2, 157-160 (2009). MSC: 05C75 05C25 PDF BibTeX XML Cite \textit{A. L. Gavrilyuk} and \textit{A. A. Makhnev}, Dokl. Math. 80, No. 2, 665--668 (2009; Zbl 1285.05153); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 428, No. 2, 157--160 (2009) Full Text: DOI OpenURL
Bang, Sejeong; Fujisaki, Tatsuya; Koolen, J. H. The spectra of the local graphs of the twisted Grassmann graphs. (English) Zbl 1172.05333 Eur. J. Comb. 30, No. 3, 638-654 (2009). MSC: 05C50 05E30 PDF BibTeX XML Cite \textit{S. Bang} et al., Eur. J. Comb. 30, No. 3, 638--654 (2009; Zbl 1172.05333) Full Text: DOI OpenURL
Curtin, Brian; Daqqa, Ibtisam The subconstituent algebra of a Latin square. (English) Zbl 1200.05260 Eur. J. Comb. 30, No. 2, 447-457 (2009). MSC: 05E30 05B15 PDF BibTeX XML Cite \textit{B. Curtin} and \textit{I. Daqqa}, Eur. J. Comb. 30, No. 2, 447--457 (2009; Zbl 1200.05260) Full Text: DOI OpenURL
Vallentin, Frank Symmetry in semidefinite programs. (English) Zbl 1165.90017 Linear Algebra Appl. 430, No. 1, 360-369 (2009). MSC: 90C22 33C90 PDF BibTeX XML Cite \textit{F. Vallentin}, Linear Algebra Appl. 430, No. 1, 360--369 (2009; Zbl 1165.90017) Full Text: DOI arXiv OpenURL
Miklavič, Štefko The Terwilliger algebra of a distance-regular graph of negative type. (English) Zbl 1225.05257 Linear Algebra Appl. 430, No. 1, 251-270 (2009). MSC: 05E30 05C12 PDF BibTeX XML Cite \textit{Š. Miklavič}, Linear Algebra Appl. 430, No. 1, 251--270 (2009; Zbl 1225.05257) Full Text: DOI arXiv OpenURL
Makhnev, A. A. On graphs in which the neighborhood of each vertex is isomorphic to the Hoffman-Singleton graph. (English. Russian original) Zbl 1202.05115 Dokl. Math. 78, No. 2, 771-773 (2008); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 422, No. 6, 735-737 (2008). MSC: 05C75 05C25 PDF BibTeX XML Cite \textit{A. A. Makhnev}, Dokl. Math. 78, No. 2, 771--773 (2008; Zbl 1202.05115); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 422, No. 6, 735--737 (2008) Full Text: DOI OpenURL
Gvozdenović, Nebojša; Laurent, Monique Computing semidefinite programming lower bounds for the (fractional) chromatic number via block-diagonalization. (English) Zbl 1213.05081 SIAM J. Optim. 19, No. 2, 592-615 (2008). MSC: 05C15 90C27 90C22 PDF BibTeX XML Cite \textit{N. Gvozdenović} and \textit{M. Laurent}, SIAM J. Optim. 19, No. 2, 592--615 (2008; Zbl 1213.05081) Full Text: DOI OpenURL
Miklavič, Štefko Leonard triples and hypercubes. (English) Zbl 1200.05263 J. Algebr. Comb. 28, No. 3, 397-424 (2008). MSC: 05E30 05C12 05C50 PDF BibTeX XML Cite \textit{Š. Miklavič}, J. Algebr. Comb. 28, No. 3, 397--424 (2008; Zbl 1200.05263) Full Text: DOI arXiv OpenURL
Curtin, B. Hyper-duality of type II Bose-Mesner algebras. (English) Zbl 1200.05259 J. Algebra Discrete Struct. 6, No. 1, 1-11 (2008). MSC: 05E30 PDF BibTeX XML Cite \textit{B. Curtin}, J. Algebra Discrete Struct. 6, No. 1, 1--11 (2008; Zbl 1200.05259) OpenURL
Curtin, Brian Inheritance of hyper-duality in imprimitive Bose-Mesner algebras. (English) Zbl 1182.05134 Discrete Math. 308, No. 14, 3003-3017 (2008). MSC: 05E30 PDF BibTeX XML Cite \textit{B. Curtin}, Discrete Math. 308, No. 14, 3003--3017 (2008; Zbl 1182.05134) Full Text: DOI OpenURL
MacLean, Mark S.; Terwilliger, Paul The subconstituent algebra of a bipartite distance-regular graph; thin modules with endpoint two. (English) Zbl 1136.05076 Discrete Math. 308, No. 7, 1230-1259 (2008). Reviewer: Alexandre A. Makhnev (Ekaterinburg) MSC: 05E30 20D15 PDF BibTeX XML Cite \textit{M. S. MacLean} and \textit{P. Terwilliger}, Discrete Math. 308, No. 7, 1230--1259 (2008; Zbl 1136.05076) Full Text: DOI arXiv OpenURL
Laurent, Monique Strengthened semidefinite programming bounds for codes. (English) Zbl 1147.90034 Math. Program. 109, No. 2-3 (B), 239-261 (2007). Reviewer: Efstratios Rappos (Athens) MSC: 90C27 90C22 05E20 94B65 PDF BibTeX XML Cite \textit{M. Laurent}, Math. Program. 109, No. 2--3 (B), 239--261 (2007; Zbl 1147.90034) Full Text: DOI Link OpenURL
Nomura, Kazumasa; Terwilliger, Paul Linear transformations that are tridiagonal with respect to both eigenbases of a Leonard pair. (English) Zbl 1119.05111 Linear Algebra Appl. 420, No. 1, 198-207 (2007). Reviewer: Hans Havlicek (Wien) MSC: 05E30 15A04 05E35 33C45 33D45 PDF BibTeX XML Cite \textit{K. Nomura} and \textit{P. Terwilliger}, Linear Algebra Appl. 420, No. 1, 198--207 (2007; Zbl 1119.05111) Full Text: DOI arXiv OpenURL
Nomura, Kazumasa; Terwilliger, Paul Balanced Leonard pairs. (English) Zbl 1119.05110 Linear Algebra Appl. 420, No. 1, 51-69 (2007). Reviewer: Hans Havlicek (Wien) MSC: 05E30 15A04 05E35 33C45 33D45 PDF BibTeX XML Cite \textit{K. Nomura} and \textit{P. Terwilliger}, Linear Algebra Appl. 420, No. 1, 51--69 (2007; Zbl 1119.05110) Full Text: DOI arXiv OpenURL
Gijswijt, Dion; Schrijver, Alexander; Tanaka, Hajime New upper bounds for nonbinary codes based on the Terwilliger algebra and semidefinite programming. (English) Zbl 1105.94027 J. Comb. Theory, Ser. A 113, No. 8, 1719-1731 (2006). MSC: 94B65 05E30 90C22 PDF BibTeX XML Cite \textit{D. Gijswijt} et al., J. Comb. Theory, Ser. A 113, No. 8, 1719--1731 (2006; Zbl 1105.94027) Full Text: DOI Link OpenURL
MacLean, Mark S.; Terwilliger, Paul Taut distance-regular graphs and the subconstituent algebra. (English) Zbl 1100.05104 Discrete Math. 306, No. 15, 1694-1721 (2006). Reviewer: Ioan Tomescu (Bucureşti) MSC: 05E30 PDF BibTeX XML Cite \textit{M. S. MacLean} and \textit{P. Terwilliger}, Discrete Math. 306, No. 15, 1694--1721 (2006; Zbl 1100.05104) Full Text: DOI arXiv OpenURL
Nomura, Kazumasa; Terwilliger, Paul The determinant of \(AA^{*} - A^{*}A\) for a Leonard pair \(A,A^{*}\). (English) Zbl 1108.15007 Linear Algebra Appl. 416, No. 2-3, 880-889 (2006). Reviewer: Hans Havlicek (Wien) MSC: 15A15 05E35 05E30 33C45 33D45 15A04 PDF BibTeX XML Cite \textit{K. Nomura} and \textit{P. Terwilliger}, Linear Algebra Appl. 416, No. 2--3, 880--889 (2006; Zbl 1108.15007) Full Text: DOI arXiv OpenURL
Schrijver, Alexander New code upper bounds from the Terwilliger algebra and semidefinite programming. (English) Zbl 1298.94152 IEEE Trans. Inf. Theory 51, No. 8, 2859-2866 (2005). MSC: 94B65 94B05 05E30 16S99 90C22 PDF BibTeX XML Cite \textit{A. Schrijver}, IEEE Trans. Inf. Theory 51, No. 8, 2859--2866 (2005; Zbl 1298.94152) Full Text: DOI OpenURL
Suzuki, Hiroshi The subconstituent algebra of a strongly regular graph. (English) Zbl 1069.05081 J. Algebr. Comb. 22, No. 1, 5-38 (2005). MSC: 05E30 PDF BibTeX XML Cite \textit{H. Suzuki}, J. Algebr. Comb. 22, No. 1, 5--38 (2005; Zbl 1069.05081) Full Text: DOI OpenURL
Caughman, John S.; Maclean, Mark S.; Terwilliger, Paul M. The Terwilliger algebra of an almost-bipartite \(P\)- and \(Q\)-polynomial association scheme. (English) Zbl 1063.05135 Discrete Math. 292, No. 1-3, 17-44 (2005). Reviewer: Alexandre A. Makhnev (Ekaterinburg) MSC: 05E30 PDF BibTeX XML Cite \textit{J. S. Caughman} et al., Discrete Math. 292, No. 1--3, 17--44 (2005; Zbl 1063.05135) Full Text: DOI arXiv OpenURL
Curtin, Brian; Nomura, Kazumasa 1-homogeneous, pseudo-1-homogeneous, and 1-thin distance-regular graphs. (English) Zbl 1060.05101 J. Comb. Theory, Ser. B 93, No. 2, 279-302 (2005). Reviewer: Alexandre A. Makhnev (Ekaterinburg) MSC: 05E30 51E12 PDF BibTeX XML Cite \textit{B. Curtin} and \textit{K. Nomura}, J. Comb. Theory, Ser. B 93, No. 2, 279--302 (2005; Zbl 1060.05101) Full Text: DOI OpenURL
Levstein, F.; Penazzi, D. The Terwilliger algebra of the dodecahedron. (English) Zbl 1082.05099 Rev. Unión Mat. Argent. 45, No. 2, 11-20 (2004). MSC: 05E30 PDF BibTeX XML Cite \textit{F. Levstein} and \textit{D. Penazzi}, Rev. Unión Mat. Argent. 45, No. 2, 11--20 (2004; Zbl 1082.05099) OpenURL
Iwamoto, Seiichi On the first subconstituent of a quadratic forms scheme. (English) Zbl 1121.05128 Kyushu J. Math. 58, No. 2, 353-371 (2004). MSC: 05E30 05C50 20G40 PDF BibTeX XML Cite \textit{S. Iwamoto}, Kyushu J. Math. 58, No. 2, 353--371 (2004; Zbl 1121.05128) Full Text: DOI OpenURL
Caughman, John S. IV Bipartite \(Q\)-polynomial distance-regular graphs. (English) Zbl 1054.05101 Graphs Comb. 20, No. 1, 47-57 (2004). Reviewer: Alexandre A. Makhnev (Ekaterinburg) MSC: 05E30 PDF BibTeX XML Cite \textit{J. S. Caughman IV}, Graphs Comb. 20, No. 1, 47--57 (2004; Zbl 1054.05101) Full Text: DOI OpenURL
Terwilliger, Paul An inequality involving the local eigenvalues of a distance-regular graph. (English) Zbl 1047.05045 J. Algebr. Comb. 19, No. 2, 143-172 (2004). Reviewer: Alexandre A. Makhnev (Ekaterinburg) MSC: 05E30 05E35 05C50 PDF BibTeX XML Cite \textit{P. Terwilliger}, J. Algebr. Comb. 19, No. 2, 143--172 (2004; Zbl 1047.05045) Full Text: DOI OpenURL
Terwilliger, Paul; Weng, Chih-wen Distance-regular graphs, pseudo primitive idempotents, and the Terwilliger algebra. (English) Zbl 1035.05104 Eur. J. Comb. 25, No. 2, 287-298 (2004). Reviewer: Alexandre Makhnev (Ekaterinburg) MSC: 05E30 PDF BibTeX XML Cite \textit{P. Terwilliger} and \textit{C.-w. Weng}, Eur. J. Comb. 25, No. 2, 287--298 (2004; Zbl 1035.05104) Full Text: DOI arXiv OpenURL
Marco, José Manuel; Parcet, Javier On the natural representation of \(S({\Omega})\) into \(L ^{2}(\mathcal{P}({\Omega)})\) : Discrete harmonics and Fourier transform. (English) Zbl 1013.05090 J. Comb. Theory, Ser. A 100, No. 1, 153-175 (2002). MSC: 05E30 33C80 PDF BibTeX XML Cite \textit{J. M. Marco} and \textit{J. Parcet}, J. Comb. Theory, Ser. A 100, No. 1, 153--175 (2002; Zbl 1013.05090) Full Text: DOI arXiv OpenURL
Go, Junie T.; Terwilliger, Paul Tight distance-regular graphs and the subconstituent algebra. (English) Zbl 1014.05070 Eur. J. Comb. 23, No. 7, 793-816 (2002). Reviewer: Alexandre A.Makhnev (Ekaterinburg) MSC: 05E30 PDF BibTeX XML Cite \textit{J. T. Go} and \textit{P. Terwilliger}, Eur. J. Comb. 23, No. 7, 793--816 (2002; Zbl 1014.05070) Full Text: DOI OpenURL
Terwilliger, Paul The subconstituent algebra of a distance-regular graph; thin modules with endpoint one. (English) Zbl 1011.05066 Linear Algebra Appl. 356, No. 1-3, 157-187 (2002). Reviewer: Alexandre A.Makhnev (Ekaterinburg) MSC: 05E30 05E35 05C50 PDF BibTeX XML Cite \textit{P. Terwilliger}, Linear Algebra Appl. 356, No. 1--3, 157--187 (2002; Zbl 1011.05066) Full Text: DOI OpenURL
Go, Junie T. The Terwilliger algebra of the hypercube. (English) Zbl 0997.05097 Eur. J. Comb. 23, No. 4, 399-429 (2002). Reviewer: Alexandre A.Makhnev (Ekaterinburg) MSC: 05E30 PDF BibTeX XML Cite \textit{J. T. Go}, Eur. J. Comb. 23, No. 4, 399--429 (2002; Zbl 0997.05097) Full Text: DOI OpenURL
Egge, Eric S. The generalized Terwilliger algebra and its finite-dimensional modules when \(d=2\). (English) Zbl 1003.05107 J. Algebra 250, No. 1, 178-216 (2002). Reviewer: Alexandre A.Makhnev (Ekaterinburg) MSC: 05E30 20C15 PDF BibTeX XML Cite \textit{E. S. Egge}, J. Algebra 250, No. 1, 178--216 (2002; Zbl 1003.05107) Full Text: DOI OpenURL
Ito, Tatsuro; Tanabe, Kenichiro; Terwilliger, Paul Some algebra related to \(P\)- and \(Q\)-polynomial association schemes. (English) Zbl 0995.05148 Barg, Alexander (ed.) et al., Codes and association schemes. DIMACS workshop, DIMACS Center, Princeton, NJ, USA, November 9-12, 1999. Providence, RI: AMS, American Mathematical Society. DIMACS, Ser. Discrete Math. Theor. Comput. Sci. 56, 167-192 (2001). Reviewer: Markus Fulmek (Wien) MSC: 05E30 15A21 33C45 PDF BibTeX XML Cite \textit{T. Ito} et al., DIMACS, Ser. Discrete Math. Theor. Comput. Sci. 56, 167--192 (2001; Zbl 0995.05148) Full Text: arXiv OpenURL
Curtin, Brian; Nomura, Kazumasa Distance-regular graphs related to the quantum enveloping algebra of \(sl(2)\). (English) Zbl 0967.05067 J. Algebr. Comb. 12, No. 1, 25-36 (2000). Reviewer: B.Baumeister (Halle) MSC: 05E30 PDF BibTeX XML Cite \textit{B. Curtin} and \textit{K. Nomura}, J. Algebr. Comb. 12, No. 1, 25--36 (2000; Zbl 0967.05067) Full Text: DOI OpenURL
Egge, Eric S. A generalization of the Terwilliger algebra. (English) Zbl 0960.05108 J. Algebra 233, No. 1, 213-252 (2000). Reviewer: Alexandre A.Makhnev (Ekaterinburg) MSC: 05E30 PDF BibTeX XML Cite \textit{E. S. Egge}, J. Algebra 233, No. 1, 213--252 (2000; Zbl 0960.05108) Full Text: DOI Link OpenURL
Curtin, Brian Almost 2-homogeneous bipartite distance-regular graphs. (English) Zbl 1002.05069 Eur. J. Comb. 21, No. 7, 865-876 (2000). MSC: 05E30 05C12 PDF BibTeX XML Cite \textit{B. Curtin}, Eur. J. Comb. 21, No. 7, 865--876 (2000; Zbl 1002.05069) Full Text: DOI OpenURL
Collins, Benjamin V. C. The Terwilliger algebra of an almost-bipartite distance-regular graph and its antipodal 2-cover. (English) Zbl 0955.05113 Discrete Math. 216, No. 1-3, 35-69 (2000). Reviewer: C.Baetica (Bucureşti) MSC: 05E30 05C12 PDF BibTeX XML Cite \textit{B. V. C. Collins}, Discrete Math. 216, No. 1--3, 35--69 (2000; Zbl 0955.05113) Full Text: DOI OpenURL
Curtin, Brian Bipartite distance-regular graphs. II. (English) Zbl 0939.05088 Graphs Comb. 15, No. 4, 377-391 (1999). MSC: 05E30 PDF BibTeX XML Cite \textit{B. Curtin}, Graphs Comb. 15, No. 4, 377--391 (1999; Zbl 0939.05088) Full Text: DOI OpenURL
Ishibashi, Haruo; Ito, Tatsuro; Yamada, Mieko Terwilliger algebras of cyclotomic schemes and Jacobi sums. (English) Zbl 0944.05101 Eur. J. Comb. 20, No. 5, 397-410 (1999). Reviewer: Vesselin Drensky (Sofia) MSC: 05E30 11T24 PDF BibTeX XML Cite \textit{H. Ishibashi} et al., Eur. J. Comb. 20, No. 5, 397--410 (1999; Zbl 0944.05101) Full Text: DOI OpenURL
Curtin, Brian Bipartite distance-regular graphs. I. (English) Zbl 0927.05083 Graphs Comb. 15, No. 2, 143-158 (1999). Reviewer: A.A.Makhnev (Ekaterinburg) MSC: 05E30 PDF BibTeX XML Cite \textit{B. Curtin}, Graphs Comb. 15, No. 2, 143--158 (1999; Zbl 0927.05083) Full Text: DOI OpenURL