The Erdo¨s-Ko-Rado theorem for vector spaces
Journal of Combinatorial Theory Series A
Tables of the association schemes of finite orthogonal groups acting on the nonisotropic points
Journal of Combinatorial Theory Series A
Splitting fields of association schemes
Journal of Combinatorial Theory Series A
Distance regular covers of the complete graph
Journal of Combinatorial Theory Series B
The Subconstituent Algebra of an Association Scheme (Part III)
Journal of Algebraic Combinatorics: An International Journal
Association Schemes and Fusion Algebras (An Introduction)
Journal of Algebraic Combinatorics: An International Journal
The Subconstituent Algebra of an Association Scheme (Part II)
Journal of Algebraic Combinatorics: An International Journal
The Subconstituent Algebra of an Association Scheme, (Part I)
Journal of Algebraic Combinatorics: An International Journal
Strongly regular designs of the second kind
European Journal of Combinatorics
The Irreducible Modules of the Terwilliger Algebras ofDoob Schemes
Journal of Algebraic Combinatorics: An International Journal
On Spin Models, Modular Invariance, and Duality
Journal of Algebraic Combinatorics: An International Journal
Split Orthogonal Arrays and Maximum Independent ResilientSystems of Functions
Designs, Codes and Cryptography
Imprimitive Q-polynomial Association Schemes
Journal of Algebraic Combinatorics: An International Journal
Association Schemes with Multiple Q-polynomial Structures
Journal of Algebraic Combinatorics: An International Journal
Bose-Mesner Algebras Related to Type II Matrices and Spin Models
Journal of Algebraic Combinatorics: An International Journal
Upper bounds on permutation codes via linear programming
European Journal of Combinatorics
A New Proof of the Assmus–Mattson Theorem for Non-BinaryCodes
Designs, Codes and Cryptography
Spin Models and Strongly Hyper-Self-Dual Bose-Mesner Algebras
Journal of Algebraic Combinatorics: An International Journal
Introduction to Coding Theory
On the optimum of Delsarte's linear program
Journal of Combinatorial Theory Series A
Designs, Graphs, Codes, and Their Links
Designs, Graphs, Codes, and Their Links
Journal of Algebraic Combinatorics: An International Journal
Designs in Product Association Schemes
Designs, Codes and Cryptography
On Harmonic Weight Enumerators of Binary Codes
Designs, Codes and Cryptography
Minimum Distance Bounds for s-Regular Codes
Designs, Codes and Cryptography
A four-class subscheme of the association scheme coming from the action of PGL(2, 4f)
European Journal of Combinatorics
Tight distance-regular graphs and the subconstituent algebra
European Journal of Combinatorics
The Terwilliger algebra of the hypercube
European Journal of Combinatorics
Journal of Computational and Applied Mathematics - Proceedings of the sixth international symposium on orthogonal polynomials, special functions and their applications
Width and dual width of subsets in polynomial association schemes
Journal of Combinatorial Theory Series A
Orthogonal polynomials arising from the wreath products of a dihedral group with a symmetric group
Journal of Combinatorial Theory Series A
Beyond the orthogonal array concept
European Journal of Combinatorics - Special issue on algebraic combinatorics: in memory of J.J. Seidel
Designs in a coset geometry: Delsarte theory revisited
European Journal of Combinatorics - Special issue on algebraic combinatorics: in memory of J.J. Seidel
Finite analogues of non-Euclidean spaces and Ramanujan graphs
European Journal of Combinatorics - Special issue on algebraic combinatorics: in memory of J.J. Seidel
There are Finitely Many Triangle-Free Distance-Regular Graphs with Degree 8, 9 or 10
Journal of Algebraic Combinatorics: An International Journal
Constructions for Permutation Codes in Powerline Communications
Designs, Codes and Cryptography
Bose-Mesner algebras attached to invertible Jones pairs
Journal of Combinatorial Theory Series A
The Terwilliger Algebra of a Distance-Regular Graph that Supports a Spin Model
Journal of Algebraic Combinatorics: An International Journal
The Terwilliger Algebra Associated with a Set of Vertices in a Distance-Regular Graph
Journal of Algebraic Combinatorics: An International Journal
Modular Data: The Algebraic Combinatorics of Conformal Field Theory
Journal of Algebraic Combinatorics: An International Journal
Association schemes from the action of PGL(2, q) fixing a nonsingular conic in PG(2, q)
Journal of Algebraic Combinatorics: An International Journal
Journal of Combinatorial Theory Series A
A direct approach to linear programming bounds for codes and tms-nets
Designs, Codes and Cryptography
New upper bounds for nonbinary codes based on the Terwilliger algebra and semidefinite programming
Journal of Combinatorial Theory Series A - Special issue in honor of Jacobus H. van Lint
Strengthened semidefinite programming bounds for codes
Mathematical Programming: Series A and B
Tight distance-regular graphs with respect to subsets
European Journal of Combinatorics
Imprimitive cometric association schemes: Constructions and analysis
Journal of Algebraic Combinatorics: An International Journal
A note on the stability number of an orthogonality graph
European Journal of Combinatorics
Two theorems concerning the Bannai-Ito conjecture
European Journal of Combinatorics
Coloring an Orthogonality Graph
SIAM Journal on Discrete Mathematics
Journal of Combinatorial Theory Series A
The spectra of the local graphs of the twisted Grassmann graphs
European Journal of Combinatorics
Non-existence of imprimitive Q-polynomial schemes of exceptional type with d=4
European Journal of Combinatorics
Distance-regular graphs and the q-tetrahedron algebra
European Journal of Combinatorics
European Journal of Combinatorics
A wedge product of association schemes
European Journal of Combinatorics
New proofs of the Assmus-Mattson theorem based on the Terwilliger algebra
European Journal of Combinatorics
A survey on spherical designs and algebraic combinatorics on spheres
European Journal of Combinatorics
European Journal of Combinatorics
European Journal of Combinatorics
Trends and lines of development in scheme theory
European Journal of Combinatorics
Permutation group approach to association schemes
European Journal of Combinatorics
Pseudocyclic association schemes and strongly regular graphs
European Journal of Combinatorics
Type-II matrices and combinatorial structures
Combinatorica
Association schemes and coding theory
IEEE Transactions on Information Theory
Improved upper bounds on sizes of codes
IEEE Transactions on Information Theory
Generalizations of Gleason's theorem on weight enumerators of self-dual codes
IEEE Transactions on Information Theory
New upper bounds on the rate of a code via the Delsarte-MacWilliams inequalities
IEEE Transactions on Information Theory
On the Shannon capacity of a graph
IEEE Transactions on Information Theory
A comparison of the Delsarte and Lovász bounds
IEEE Transactions on Information Theory
New code upper bounds from the Terwilliger algebra and semidefinite programming
IEEE Transactions on Information Theory
A strengthening of the Assmus-Mattson theorem
IEEE Transactions on Information Theory
A Dual Plotkin Bound for (T,M,S) -Nets
IEEE Transactions on Information Theory
Ramanujan graphs on cosets of PGL2(Fq)
Finite Fields and Their Applications
Representations of finite association schemes
European Journal of Combinatorics
Nonexistence of exceptional imprimitive Q-polynomial association schemes with six classes
European Journal of Combinatorics
Classification of commutative association schemes with almost commutative Terwilliger algebras
Journal of Algebraic Combinatorics: An International Journal
On almost distance-regular graphs
Journal of Combinatorial Theory Series A
Journal of Combinatorial Theory Series A
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Association schemes were originally introduced by Bose and his co-workers in the design of statistical experiments. Since that point of inception, the concept has proved useful in the study of group actions, in algebraic graph theory, in algebraic coding theory, and in areas as far afield as knot theory and numerical integration. This branch of the theory, viewed in this collection of surveys as the ''commutative case'', has seen significant activity in the last few decades. The goal of the present survey is to discuss the most important new developments in several directions, including Gelfand pairs, cometric association schemes, Delsarte Theory, spin models and the semidefinite programming technique. The narrative follows a thread through this list of topics, this being the contrast between combinatorial symmetry and group-theoretic symmetry, culminating in Schrijver's SDP bound for binary codes (based on group actions) and its connection to the Terwilliger algebra (based on combinatorial symmetry). We propose this new role of the Terwilliger algebra in Delsarte Theory as a central topic for future work.