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Journal of Combinatorial Theory, Series A, ISSN 0097-3165, 08/2019, Volume 166, pp. 297 - 314
Let Γ denote a finite, undirected, connected graph, with vertex set X. Fix a vertex x∈X. Associated with x is a certain subalgebra T=T(x) of MatX(C), called... 
Quasi-isomorphism | Quantum decomposition | Subconstituent algebra | Quantum adjacency algebra | Terwilliger algebra | MATHEMATICS | UPPER-BOUNDS | DISTANCE-REGULAR GRAPH | Algebra
Journal Article
Linear Algebra and Its Applications, ISSN 0024-3795, 05/2016, Volume 496, pp. 307 - 330
Let Γ denote a bipartite distance-regular graph with diameter D≥4 and valency k≥3. Let X denote the vertex set of Γ, and let A denote the adjacency matrix of... 
Terwilliger algebra | Distance-regular graphs | Subconstituent algebra
Journal Article
数学年刊:B辑英文版, ISSN 0252-9599, 2015, Volume 36, Issue 2, pp. 293 - 306
Let D be an integer at least 3 and let H(D, 2) denote the hypercube. It is known that H(D, 2) is a Q-polynomial distance-regular graph with diameter D, and its... 
多项式 | 四面体 | 代数 | 距离正则图 | 标准模块 | 超立方体 | 特征值序列 | 发电机 | 05E30 | Tetrahedron algebra | Onsager algebra | 05C50 | Hypercube | 17B65 | Distance-regular graph | Mathematics, general | Mathematics | Applications of Mathematics | MATHEMATICS | IRREDUCIBLE MODULES | SUBCONSTITUENT ALGEBRA | DISTANCE-REGULAR GRAPHS | POLYNOMIAL ASSOCIATION SCHEMES | LOOP ALGEBRA | THIN | TERWILLIGER ALGEBRAS | Algebra
Journal Article
Kyushu Journal of Mathematics, ISSN 1340-6116, 2009, Volume 64, Issue 1, pp. 81 - 144
Motivated by investigations of the tridiagonal pairs of linear transformations, we introduce the augmented tridiagonal algebra Τq. This is an... 
tridiagonal pair | Leonard pair | P-and Q-polynomial association scheme | Terwilliger algebra | tridiagonal algebra | q-Onsager algebra | Q-Onsager algebra | Tridiagonal algebra | P- and Q-polynomial association scheme | Tridiagonal pair | MATHEMATICS
Journal Article
Linear Algebra and Its Applications, ISSN 0024-3795, 12/2016, Volume 510, pp. 311 - 328
Let F={0,1,2,3} and define the set K={K0,K1,K2} of relations on F such that (x,y)∈Ki if and only if x−y≡±i(mod 4). Let n be a positive integer. We consider the... 
Specht module | Lee association scheme | Special linear Lie algebra | Schur–Weyl duality | Terwilliger algebra
Journal Article
Graphs and Combinatorics, ISSN 0911-0119, 1/2017, Volume 33, Issue 1, pp. 149 - 156
Analyzing Terwilliger (J Algebr Comb 2:177–210, 1993, Example 6.1(1), page 198), we make an observation on parameters of Leonard systems that arise from... 
Johnson scheme | 05 E 18 | 33 C 80 | Mathematics | Engineering Design | Combinatorics | Terwilliger algebra | 05 E 30 | Leonard system | MATHEMATICS | SUBCONSTITUENT ALGEBRA | ASSOCIATION SCHEME | Analysis | Algebra | Theorems | Parameters | Modules | Graphs | Systems analysis | Combinatorial analysis
Journal Article
Discrete Mathematics, ISSN 0012-365X, 03/2013, Volume 313, Issue 5, pp. 698 - 703
In [F. Levstein, C. Maldonado, The Terwilliger algebra of the Johnson schemes, Discrete Math. 307 (2007) 1621–1635], Levstein and Maldonado computed the... 
Terwilliger algebra | Odd graph | MATHEMATICS | ASSOCIATION SCHEME | Algebra
Journal Article
Linear Algebra and Its Applications, ISSN 0024-3795, 11/2013, Volume 439, Issue 10, pp. 3184 - 3240
We study a relationship between Q-polynomial distance-regular graphs and the double affine Hecke algebra of type (C1∨,C1). Let Γ denote a Q-polynomial... 
Distance-regular graph | Q-polynomial | DAHA of rank one | Leonard system | MATHEMATICS, APPLIED | RESPECT | TERWILLIGER ALGEBRA | SET | EIGENBASIS | 2 LINEAR TRANSFORMATIONS | SCHEMES | Algebra
Journal Article
Discrete Mathematics, ISSN 0012-365X, 08/2014, Volume 328, Issue 1, pp. 54 - 62
In Levstein and Maldonado (2007), the Terwilliger algebra of the Johnson scheme J(n,d) was determined when n≥3d. In this paper, we determine the Terwilliger... 
Johnson scheme | Terwilliger algebra | Association scheme | MATHEMATICS | SUBCONSTITUENT ALGEBRA | Algebra | Mathematical analysis
Journal Article
IEEE Transactions on Information Theory, ISSN 0018-9448, 08/2005, Volume 51, Issue 8, pp. 2859 - 2866
Journal Article
LINEAR ALGEBRA AND ITS APPLICATIONS, ISSN 0024-3795, 12/2016, Volume 510, pp. 311 - 328
Let F = {0, 1, 2, 3} and define the set K = {K-0, K-1, K-2} of relations on F such that (x, y) epsilon K-i if and only if x - y equivalent to +/- i (mod 4).... 
POLYNOMIALS | MATHEMATICS | Lee association scheme | Special linear Lie algebra | MATHEMATICS, APPLIED | UPPER-BOUNDS | CODES | SUBCONSTITUENT ALGEBRA | Specht module | Schur-Weyl duality | Terwilliger algebra
Journal Article
Discrete Mathematics, ISSN 0012-365X, 03/2017, Volume 340, Issue 3, pp. 452 - 466
Let Γ denote a bipartite distance-regular graph with diameter D≥4 and valency k≥3. Let X denote the vertex set of Γ, and let A denote the adjacency matrix of... 
Terwilliger algebra | Distance-regular graphs | Subconstituent algebra
Journal Article
Linear Algebra and Its Applications, ISSN 0024-3795, 04/2015, Volume 471, pp. 427 - 448
Let Jq(n,m) denote the Grassmann graph with vertex set X and diameter min⁡{m,n−m}. Fix a vertex x∈X. Let T=T(x) denote the Terwilliger algebra of Jq(n,m)... 
Grassmann graph | Quantum enveloping algebra | Leonard pair | q-Tetrahedron algebra | Terwilliger algebra | MATHEMATICS | MATHEMATICS, APPLIED | IRREDUCIBLE MODULES | SUBCONSTITUENT ALGEBRA | ASSOCIATION SCHEME | DISTANCE-REGULAR GRAPHS | Algebra
Journal Article
Linear Algebra and Its Applications, ISSN 0024-3795, 11/2015, Volume 484, pp. 435 - 456
By a Leonard triple, we mean a triple of diagonalizable operators on a finite-dimensional vector space such that for each operator, there is an ordering of an... 
Racah algebra | Distance-regular graphs | Leonard triples | Terwilliger algebra | POLYNOMIALS | MATHEMATICS | MATHEMATICS, APPLIED | TRANSFORMATIONS | TERWILLIGER ALGEBRAS | Algebra
Journal Article
ARS MATHEMATICA CONTEMPORANEA, ISSN 1855-3966, 2019, Volume 17, Issue 1, pp. 185 - 202
In this paper we consider a distance-regular graph Gamma. Fix a vertex x of Gamma and consider the corresponding subconstituent algebra T = T(x). The algebra T... 
distance-regular graph | MATHEMATICS | THIN MODULES | MATHEMATICS, APPLIED | UPPER-BOUNDS | Subconstituent algebra | Terwilliger algebra
Journal Article
Journal of Algebraic Combinatorics, ISSN 0925-9899, 8/2018, Volume 48, Issue 1, pp. 77 - 118
Let $$\varGamma $$ Γ be a distance-semiregular graph on Y, and let $$D^Y$$ DY be the diameter of $$\varGamma $$ Γ on Y. Let $$\varDelta $$ Δ be the halved... 
Incidence graph | Distance-semiregular graph | Convex and Discrete Geometry | Hamming graph | Distance-regular graph | Mathematics | Order, Lattices, Ordered Algebraic Structures | Group Theory and Generalizations | Combinatorics | Computer Science, general | Terwilliger algebra | MATHEMATICS | SUBCONSTITUENT ALGEBRA | ASSOCIATION SCHEME | Algebra
Journal Article
Linear Algebra and Its Applications, ISSN 0024-3795, 03/2016, Volume 493, pp. 146 - 163
The Terwilliger algebra of an association scheme of order n introduced in [13] is a subalgebra of the matrix algebra of all n×n matrices. Terwilliger algebras... 
Terwilliger algebras | Bose–Mesner algebras | Primitive central idempotents | Association schemes | Coherent configurations | Bose-Mesner algebras | MATHEMATICS | MATHEMATICS, APPLIED | Algebra
Journal Article
LINEAR ALGEBRA AND ITS APPLICATIONS, ISSN 0024-3795, 05/2016, Volume 496, pp. 307 - 330
Let Gamma denote a bipartite distance-regular graph with diameter D >= 4 and valency k >= 3. Let X denote the vertex set of Gamma, and let A denote the... 
MATHEMATICS | MATHEMATICS, APPLIED | Distance-regular graphs | Subconstituent algebra | Terwilliger algebra
Journal Article
DISCRETE MATHEMATICS, ISSN 0012-365X, 03/2017, Volume 340, Issue 3, pp. 452 - 466
Let Gamma denote a bipartite distance-regular graph with diameter D >= 4 and valency k >= 3. Let X denote the vertex set of Gamma, and let A denote the... 
MATHEMATICS | Distance-regular graphs | Subconstituent algebra | Terwilliger algebra
Journal Article
Linear Algebra and Its Applications, ISSN 0024-3795, 02/2014, Volume 443, pp. 164 - 183
Let J(n,m) denote the Johnson graph with vertex set X. Fix a vertex x∈X. Let T=T(x) denote the Terwilliger algebra of J(n,m) corresponding to x. In this paper... 
Johnson graph | Universal enveloping algebra | Leonard pair | Terwilliger algebra | Leonard system | MATHEMATICS, APPLIED | IRREDUCIBLE MODULES | SUBCONSTITUENT ALGEBRA | ASSOCIATION SCHEME | LOOP ALGEBRA | DISTANCE-REGULAR GRAPH | Algebra
Journal Article
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