Investigations in Algebraic Theory of Combinatorial Objects

X Köchendorffer, L.A. Kalu:lnin and their students in the 50s and 60s. Nowadays the most deeply developed is the theory of binary invariant relations and their combinatorial approximations. These combinatorial approximations arose repeatedly during this century under various names (Hecke algebras, centralizer rings, association schemes, coherent configurations, cellular rings, etc.-see the first paper of the collection for details) andin various branches of mathematics, both pure and applied. One of these approximations, the theory of cellular rings (cellular algebras), was developed at the end of the 60s by B. Yu. Weisfeiler and A.A. Leman in the course of the first serious attempt to study the complexity of the graph isomorphism problem, one of the central problems in the modern theory of combinatorial algorithms. At roughly the same time G.M. Adelson-Velskir, V.L. Arlazarov, I.A. Faradtev and their colleagues had developed a rather efficient tool for the constructive enumeration of combinatorial objects based on the branch and bound method. By means of this tool a number of "sports-like" results were obtained. Some of these results are still unsurpassed.

Inhalt

Series Editor's Preface. Preface to the English Edition. Preface to the Russian Edition. Part 1: Cellular Rings. 1.1. Cellular Rings and Groups of Automorphisms of Graphs; I.A. Faradzev, M.H. Klin, M.H. Muzichuk. 1.2 On p-Local Analysis of Permutation Groups; V.A. Ustimenko. 1.3. Amorphic Cellular Rings; Ja. Ju. Gol'fand, A.V. Ivanov, M.H. Klin. 1.4 The Subschemes of the Hamming Scheme; M.E. Muzichuk. 1.5. A Description of Subrings in V(Sp1 x Sp2 x ... x Spm); Ja. Ju. Gol'fand. 1.6. Cellular Subrings of the Symmetric Square of a Cellular Ring of Rank 3; I.A. Faradzev. 1.7. The Intersection Numbers of the Hecke Algebras H(PGLn(q),BWjB); V.A. Ustimenko. 1.8. Ranks and Subdegrees of the Symmetric Groups Acting on Partitions; I.A. Faradzev, A.V. Ivanov. 1.9. Computation of Lengths of Orbits of a Subgroup in a Transitive Permutation Group; A.A. Ivanov. Part 2: Distance-Transitive Graphs. 2.1. Distance-Transitive Graphs and Their Classification; A.A. Ivanov. 2.2. On Some Local Characteristics of Distance-Transitive Graphs; A.V. Ivanov. 2.3. Action of the Group M12 on Hadamard Matrices; I.V. Chuvaeva, A.A. Ivanov. 2.4. Construction of an Automorphic Graph on 280 Vertices Using Finite Geometries; F.L. Tchuda. Part 3: Amalgams and Diagram Geometries. 3.1. Applications of Group Amalgams to Algebraic Graph Theory; A.A. Ivanov, S.V. Shpectorov. 3.2. A Geometric Characterization of the Group M22; S.V. Shpectorov. 3.3. Bi-Primitive Cubic Graphs; M.E. Lofinova, A.A. Ivanov. 3.4. On Some Properties of Geometries of Chevalley Groups and Their Generalizations; V.A. Ustimenko. Subject Index.