Investigations in Algebraic Theory of Combinatorial Objects

1. Front Matter

   Pages i-xi

   PDF

2. Cellular Rings

   1. Cellular Rings and Groups of Automorphisms of Graphs

      • I. A. Faradžev, M. H. Klin, M. E. Muzichuk

      Pages 1-152

   2. On p-Local Analysis of Permutation Groups

      • V. A. Ustimenko

      Pages 153-166

   3. Amorphic Cellular Rings

      • Ja. Ju. Gol’fand, A. V. Ivanov, M. H. Klin

      Pages 167-186

   4. The Subschemes of the Hamming Scheme

      • M. E. Muzichuk

      Pages 187-208

   5. A Description of Subrings in \( V\left( {S_{p_1 } \times S_{p_2 } \times \cdots \times S_{p_m } } \right)\)

      • Ja. Ju. Gol’fand

      Pages 209-223

   6. Cellular Subrings of the Symmetric Square of a Cellular Ring of Rank 3

      • I. A. Faradžev

      Pages 225-249

   7. The Intersection Numbers of the Hecke Algebras H(PGL _n (q), BW _j B)

      • V. A. Ustimenko

      Pages 251-263

   8. Ranks and Subdegrees of the Symmetric Groups Acting on Partitions

      • I. A. Faradžev, A. V. Ivanov

      Pages 265-273

   9. Computation of Lengths of Orbits of a Subgroup in a Transitive Permutation Group

      • A. A. Ivanov

      Pages 275-282

3. Distance-Transitive Graphs

   1. Distance-Transitive Graphs and Their Classification

      • A. A. Ivanov

      Pages 283-378

   2. On Some Local Characteristics of Distance-Transitive Graphs

      • A. V. Ivanov

      Pages 379-394

   3. Action of the Group M ₁₂ on Hadamard Matrices

      • I. V. Chuvaeva, A. A. Ivanov

      Pages 395-408

   4. Construction of an Automorphic Graph on 280 Vertices Using Finite Geometries

      • F. L. Tchuda

      Pages 409-415

4. Amalgams and Diagram Geometries

   1. Applications of Group Amalgams to Algebraic Graph Theory

      • A. A. Ivanov, S. V. Shpectorov

      Pages 417-441

   2. A Geometric Characterization of the Group M ₂₂

      • S. V. Shpectorov

      Pages 443-457

   3. Bi-Primitive Cubic Graphs

      • M. E. Iofinova, A. A. Ivanov

      Pages 459-472

   4. On Some Properties of Geometries of Chevalley Groups and Their Generalizations

      • V. A. Ustimenko

      Pages 473-505

5. Back Matter

   Pages 507-510

   PDF

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.

• Graph
• Graph theory
• Node
• Permutation
• Vertices
• algebra
• classification

• Institute for System Studies, Moscow, Russia

  I. A. Faradžev, A. A. Ivanov, M. H. Klin

• Villanova University, Villanova, USA

  A. J. Woldar

Policies and ethics