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
Koohestani, Masoumeh; Obata, Nobuaki; Tanaka, Hajime Scaling limits for the Gibbs states on distance-regular graphs with classical parameters. (English) Zbl 07453208 SIGMA, Symmetry Integrability Geom. Methods Appl. 17, Paper 104, 22 p. (2021). MSC: 46L53 60F05 05E30 PDF BibTeX XML Cite \textit{M. Koohestani} et al., SIGMA, Symmetry Integrability Geom. Methods Appl. 17, Paper 104, 22 p. (2021; Zbl 07453208) Full Text: DOI arXiv 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
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
Nomura, Kazumasa; Terwilliger, Paul Totally bipartite tridiagonal pairs. (English) Zbl 07373356 Electron. J. Linear Algebra 37, 434-491 (2021). MSC: 17B37 15A21 PDF BibTeX XML Cite \textit{K. Nomura} and \textit{P. Terwilliger}, Electron. J. Linear Algebra 37, 434--491 (2021; Zbl 07373356) Full Text: arXiv Link 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
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
Ustimenko, V. On small world non-Sunada twins and cellular Voronoi diagrams. (English) Zbl 1473.05191 Algebra Discrete Math. 30, No. 1, 118-142 (2020). MSC: 05C50 05C82 51E24 PDF BibTeX XML Cite \textit{V. Ustimenko}, Algebra Discrete Math. 30, No. 1, 118--142 (2020; Zbl 1473.05191) Full Text: DOI 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
Tanaka, Hajime; Wang, Tao The Terwilliger algebra of the twisted Grassmann graph: the thin case. (English) Zbl 1451.05252 Electron. J. Comb. 27, No. 4, Research Paper P4.15, 22 p. (2020). MSC: 05E30 16S50 PDF BibTeX XML Cite \textit{H. Tanaka} and \textit{T. Wang}, Electron. J. Comb. 27, No. 4, Research Paper P4.15, 22 p. (2020; Zbl 1451.05252) Full Text: DOI arXiv 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
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
Ito, Tatsuro TD-pairs and the \(q\)-Onsager algebra. (English. Japanese original) Zbl 1475.17008 Sugaku Expo. 32, No. 2, 205-232 (2019); translation from Sūgaku 65, No. 1, 69-92 (2013). MSC: 17A99 15A30 17B37 PDF BibTeX XML Cite \textit{T. Ito}, Sugaku Expo. 32, No. 2, 205--232 (2019; Zbl 1475.17008); translation from Sūgaku 65, No. 1, 69--92 (2013) Full Text: DOI 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
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
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
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
Lee, Jae-Ho Nonsymmetric Askey-Wilson polynomials and \(Q\)-polynomial distance-regular graphs. (English) Zbl 1352.05094 J. Comb. Theory, Ser. A 147, 75-118 (2017). MSC: 05C31 05C12 33C45 42C05 PDF BibTeX XML Cite \textit{J.-H. Lee}, J. Comb. Theory, Ser. A 147, 75--118 (2017; Zbl 1352.05094) Full Text: DOI arXiv 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
Liu, Wen The attenuated space poset \(\mathcal{A}_q(N, M)\). (English) Zbl 1346.05026 Linear Algebra Appl. 506, 244-273 (2016). MSC: 05B25 15A04 17B37 PDF BibTeX XML Cite \textit{W. Liu}, Linear Algebra Appl. 506, 244--273 (2016; Zbl 1346.05026) Full Text: DOI arXiv 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
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
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
Hou, Bo; Gao, Suogang Hypercube and tetrahedron algebra. (English) Zbl 1310.05219 Chin. Ann. Math., Ser. B 36, No. 2, 293-306 (2015). MSC: 05E30 05C50 05C12 17B65 PDF BibTeX XML Cite \textit{B. Hou} and \textit{S. Gao}, Chin. Ann. Math., Ser. B 36, No. 2, 293--306 (2015; Zbl 1310.05219) 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
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
Morales, John Vincent S.; Pascasio, Arlene A. An action of the tetrahedron algebra on the standard module for the Hamming graphs and Doob graphs. (English) Zbl 1306.05255 Graphs Comb. 30, No. 6, 1513-1527 (2014). MSC: 05E30 05C50 05C12 15A04 33C45 PDF BibTeX XML Cite \textit{J. V. S. Morales} and \textit{A. A. Pascasio}, Graphs Comb. 30, No. 6, 1513--1527 (2014; Zbl 1306.05255) 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
Terwilliger, Paul; Žitnik, Arjana Distance-regular graphs of \(q\)-Racah type and the universal Askey-Wilson algebra. (English) Zbl 1295.05100 J. Comb. Theory, Ser. A 125, 98-112 (2014). MSC: 05C12 05E30 05E15 PDF BibTeX XML Cite \textit{P. Terwilliger} and \textit{A. Žitnik}, J. Comb. Theory, Ser. A 125, 98--112 (2014; Zbl 1295.05100) Full Text: DOI arXiv 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
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
Lee, Jae-Ho \(Q\)-polynomial distance-regular graphs and a double affine Hecke algebra of rank one. (English) Zbl 1282.05221 Linear Algebra Appl. 439, No. 10, 3184-3240 (2013). MSC: 05E30 20C08 33D80 PDF BibTeX XML Cite \textit{J.-H. Lee}, Linear Algebra Appl. 439, No. 10, 3184--3240 (2013; Zbl 1282.05221) 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
Suda, Sho New parameters of subsets in polynomial association schemes. (English) Zbl 1232.05245 J. Comb. Theory, Ser. A 119, No. 1, 117-134 (2012). MSC: 05E30 PDF BibTeX XML Cite \textit{S. Suda}, J. Comb. Theory, Ser. A 119, No. 1, 117--134 (2012; Zbl 1232.05245) 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
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
Kim, Joohyung A duality between pairs of split decompositions for a Q-polynomial distance-regular graph. (English) Zbl 1231.05299 Discrete Math. 310, No. 12, 1828-1834 (2010). MSC: 05E30 05C12 05C25 PDF BibTeX XML Cite \textit{J. Kim}, Discrete Math. 310, No. 12, 1828--1834 (2010; Zbl 1231.05299) Full Text: DOI arXiv OpenURL
Martin, William J.; Tanaka, Hajime Commutative association schemes. (English) Zbl 1228.05317 Eur. J. Comb. 30, No. 6, 1497-1525 (2009). MSC: 05E30 PDF BibTeX XML Cite \textit{W. J. Martin} and \textit{H. Tanaka}, Eur. J. Comb. 30, No. 6, 1497--1525 (2009; Zbl 1228.05317) Full Text: DOI arXiv OpenURL
Tanaka, Hajime A bilinear form relating two Leonard systems. (English) Zbl 1228.05320 Linear Algebra Appl. 431, No. 10, 1726-1739 (2009). MSC: 05E30 05E10 33C45 33D45 PDF BibTeX XML Cite \textit{H. Tanaka}, Linear Algebra Appl. 431, No. 10, 1726--1739 (2009; Zbl 1228.05320) Full Text: DOI arXiv OpenURL
Ito, Tatsuro; Terwilliger, Paul Distance-regular graphs of \(q\)-Racah type and the \(q\)-tetrahedron algebra. (English) Zbl 1206.05103 Mich. Math. J. 58, No. 1, 241-254 (2009). Reviewer: Stefano Capparelli (Roma) MSC: 05E30 17B37 PDF BibTeX XML Cite \textit{T. Ito} and \textit{P. Terwilliger}, Mich. Math. J. 58, No. 1, 241--254 (2009; Zbl 1206.05103) Full Text: DOI arXiv OpenURL
Tanaka, Hajime New proofs of the Assmus-Mattson theorem based on the Terwilliger algebra. (English) Zbl 1220.94052 Eur. J. Comb. 30, No. 3, 736-746 (2009). MSC: 94B05 05E30 05B05 PDF BibTeX XML Cite \textit{H. Tanaka}, Eur. J. Comb. 30, No. 3, 736--746 (2009; Zbl 1220.94052) Full Text: DOI arXiv OpenURL
Ito, Tatsuro; Terwilliger, Paul Distance-regular graphs and the \(q\)-tetrahedron algebra. (English) Zbl 1193.17008 Eur. J. Comb. 30, No. 3, 682-697 (2009). Reviewer: Stefano Capparelli (Roma) MSC: 17B37 05E30 PDF BibTeX XML Cite \textit{T. Ito} and \textit{P. Terwilliger}, Eur. J. Comb. 30, No. 3, 682--697 (2009; Zbl 1193.17008) Full Text: DOI arXiv OpenURL
Kim, Joohyung Some matrices associated with the split decomposition for a \(Q\)-polynomial distance-regular graph. (English) Zbl 1213.05169 Eur. J. Comb. 30, No. 1, 96-113 (2009). MSC: 05C50 05C70 05E30 PDF BibTeX XML Cite \textit{J. Kim}, Eur. J. Comb. 30, No. 1, 96--113 (2009; Zbl 1213.05169) 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
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
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
Lang, Michael S.; Terwilliger, Paul M. Almost-bipartite distance-regular graphs with the \(Q\)-polynomial property. (English) Zbl 1124.05095 Eur. J. Comb. 28, No. 1, 258-265 (2007). Reviewer: Udo Ott (Braunschweig) MSC: 05E30 05E35 05C50 PDF BibTeX XML Cite \textit{M. S. Lang} and \textit{P. M. Terwilliger}, Eur. J. Comb. 28, No. 1, 258--265 (2007; Zbl 1124.05095) Full Text: DOI arXiv 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
Suzuki, Hiroshi The geometric girth of a distance-regular graph having certain thin irreducible modules for the Terwilliger algebra. (English) Zbl 1085.05071 Eur. J. Comb. 27, No. 2, 235-254 (2006). Reviewer: Mohammad-Reza Darafsheh (Tehran) MSC: 05E30 PDF BibTeX XML Cite \textit{H. Suzuki}, Eur. J. Comb. 27, No. 2, 235--254 (2006; Zbl 1085.05071) Full Text: DOI OpenURL
Levstein, F.; Maldonado, C.; Penazzi, D. The Terwilliger algebra of a Hamming scheme \(H(d,q)\). (English) Zbl 1078.05091 Eur. J. Comb. 27, No. 1, 1-10 (2006). MSC: 05E30 PDF BibTeX XML Cite \textit{F. Levstein} et al., Eur. J. Comb. 27, No. 1, 1--10 (2006; Zbl 1078.05091) Full Text: DOI OpenURL
Terwilliger, Paul Two linear transformations each tridiagonal with respect to an eigenbasis of the other; the TD-D canonical form and the LB-UB canonical form. (English) Zbl 1079.15005 J. Algebra 291, No. 1, 1-45 (2005). Reviewer: Yueh-er Kuo (Knoxville) MSC: 15A04 15A21 PDF BibTeX XML Cite \textit{P. Terwilliger}, J. Algebra 291, No. 1, 1--45 (2005; Zbl 1079.15005) Full Text: DOI arXiv 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
Terwilliger, Paul; Vidunas, Raimundas Leonard pairs and the Askey-Wilson relations. (English) Zbl 1062.33018 J. Algebra Appl. 3, No. 4, 411-426 (2004). Reviewer: Stamatis Koumandos (Nicosia) MSC: 33D45 05A30 15A03 PDF BibTeX XML Cite \textit{P. Terwilliger} and \textit{R. Vidunas}, J. Algebra Appl. 3, No. 4, 411--426 (2004; Zbl 1062.33018) Full Text: DOI arXiv 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
Terwilliger, Paul Leonard pairs from 24 points of view. (English) Zbl 1040.05030 Rocky Mt. J. Math. 32, No. 2, 827-888 (2002). Reviewer: Frank De Clerck (Gent) MSC: 05E30 33C45 33D45 05E35 PDF BibTeX XML Cite \textit{P. Terwilliger}, Rocky Mt. J. Math. 32, No. 2, 827--888 (2002; Zbl 1040.05030) Full Text: DOI arXiv Link 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
Terwilliger, Paul Two linear transformations each tridiagonal with respect to an eigenbasis of the other. (English) Zbl 0980.05054 Linear Algebra Appl. 330, No. 1-3, 149-203 (2001). Reviewer: Patrick Solé (Sophia Antipolis) MSC: 05E35 05E30 15A04 33C45 33D45 PDF BibTeX XML Cite \textit{P. Terwilliger}, Linear Algebra Appl. 330, No. 1--3, 149--203 (2001; Zbl 0980.05054) Full Text: DOI arXiv 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 Distance-regular graphs which support a spin model are thin. (English) Zbl 0929.05095 Discrete Math. 197-198, 205-216 (1999). Reviewer: Alexander A.Ivanov (London) MSC: 05E30 PDF BibTeX XML Cite \textit{B. Curtin}, Discrete Math. 197--198, 205--216 (1999; Zbl 0929.05095) Full Text: DOI OpenURL
Caughman, John S. IV The Terwilliger algebras of bipartite \(P\)- and \(Q\)-polynomial schemes. (English) Zbl 0924.05067 Discrete Math. 196, No. 1-3, 65-95 (1999). Reviewer: A.A.Makhnev (Ekaterinburg) MSC: 05E30 PDF BibTeX XML Cite \textit{J. S. Caughman IV}, Discrete Math. 196, No. 1--3, 65--95 (1999; Zbl 0924.05067) Full Text: DOI OpenURL
Curtin, Brian 2-homogeneous bipartite distance-regular graphs. (English) Zbl 0958.05143 Discrete Math. 187, No. 1-3, 39-70 (1998). MSC: 05E30 05C12 PDF BibTeX XML Cite \textit{B. Curtin}, Discrete Math. 187, No. 1--3, 39--70 (1998; Zbl 0958.05143) Full Text: DOI OpenURL
Collins, Benjamin V. C. The girth of a thin distance-regular graph. (English) Zbl 0878.05084 Graphs Comb. 13, No. 1, 21-30 (1997). Reviewer: R.E.L.Aldred (Dunedin) MSC: 05E30 51E12 05C12 PDF BibTeX XML Cite \textit{B. V. C. Collins}, Graphs Comb. 13, No. 1, 21--30 (1997; Zbl 0878.05084) Full Text: DOI OpenURL
Ishibashi, Haruo The Terwilliger algebras of certain association schemes over the Galois rings of characteristic 4. (English) Zbl 0852.05081 Graphs Comb. 12, No. 1, 39-54 (1996). Reviewer: N.I.Osetinski (Moskva) MSC: 05E30 13J99 PDF BibTeX XML Cite \textit{H. Ishibashi}, Graphs Comb. 12, No. 1, 39--54 (1996; Zbl 0852.05081) Full Text: DOI OpenURL
Dickie, Garth A. Twice Q-polynomial distance-regular graphs are thin. (English) Zbl 0852.05085 Eur. J. Comb. 16, No. 6, 555-560 (1995). Reviewer: V.A.Ufnarovski (Lund) MSC: 05E30 PDF BibTeX XML Cite \textit{G. A. Dickie}, Eur. J. Comb. 16, No. 6, 555--560 (1995; Zbl 0852.05085) Full Text: DOI OpenURL