An algebraic approach to association schemes
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Publication:1922107
DOI10.1007/BFb0097032zbMath0857.05100OpenAlexW599879082MaRDI QIDQ1922107
Publication date: 15 September 1996
Published in: Lecture Notes in Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/bfb0097032
group algebrasassociation schemesgeneralized polygonsintersection numbersgeneralized quadranglesrepresentation theorybuildingssemisimplicitypolaritiesstructure constantsMaschke theoremCoxeter schemesfinite generalized polygonsgeneralized hexagonscomplex productconstrained schemesgenerators of schemes
Research exposition (monographs, survey articles) pertaining to combinatorics (05-02) Association schemes, strongly regular graphs (05E30) Generalized quadrangles and generalized polygons in finite geometry (51E12) Combinatorial aspects of finite geometries (05B25) Buildings and the geometry of diagrams (51E24)
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Characterization of association schemes by equitable partitions ⋮ Tamaschke's results on Schur rings and a generalization of association schemes ⋮ On some p-transitive association schemes ⋮ Semisimplicity of adjacency algebras of coherent configurations ⋮ Weakly distance-regular digraphs of valency three. I ⋮ Thin weakly distance-regular digraphs ⋮ Weakly distance-regular digraphs of one type of arcs ⋮ Characters of association schemes containing a strongly normal closed subset of prime index ⋮ A family of non-Schurian \(p\)-Schur rings over groups of order \(p^3\) ⋮ Non-commutative association schemes and their fusion association schemes ⋮ The exchange condition for association schemes ⋮ Enumerating big orbits and an application: \(B\) acting on the cosets of \(Fi_{23}\). ⋮ Indecomposability of modular standard modules of Schurian association schemes and \(p\)-schemes ⋮ Association schemes on 28 points as mergings of a half-homogeneous coherent configuration ⋮ On generalized projective spaces operating on sets ⋮ Modular adjacency algebras, standard representations, and \(p\)-ranks of cyclotomic association schemes ⋮ Modular representation theory of BIB designs ⋮ On association schemes with multiplicities 1 or a prime p ⋮ An algebraic approach to Erdős-Ko-Rado sets of flags in spherical buildings ⋮ Investigations on association schemes with elementary abelian thin residue ⋮ Weakly distance-regular digraphs of valency three, II ⋮ Every 4-equivalenced association scheme is Frobenius ⋮ Indecomposable decompositions of modular standard modules for two families of association schemes ⋮ The number of ideals of \(\mathbb{Z} [x\) containing \(x(x-\alpha)(x-\beta)\) with given index] ⋮ On \(p\)-covalenced association schemes ⋮ Clifford theory for association schemes. 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