Investigations in Algebraic Theory of Combinatorial Objects

✍ Scribed by I. A. Faradžev, M. H. Klin, M. E. Muzichuk (auth.), I. A. Faradžev, A. A. Ivanov, M. H. Klin, A. J. Woldar (eds.)

• Publisher: Springer Netherlands
• Year: 1994
• Tongue: English
• Leaves: 513
• Series: Mathematics and Its Applications 84
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages i-xi
Cellular Rings and Groups of Automorphisms of Graphs....Pages 1-152
On p -Local Analysis of Permutation Groups....Pages 153-166
Amorphic Cellular Rings....Pages 167-186
The Subschemes of the Hamming Scheme....Pages 187-208
A Description of Subrings in % MathType!MTEF!2!1!+- % feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOvamaabm % aabaGaam4uamaaBaaaleaacaWGWbWaaSbaaWqaaiaaigdaaeqaaaWc % beaakiabgEna0kaadofadaWgaaWcbaGaamiCamaaBaaameaacaaIYa % aabeaaaSqabaGccqGHxdaTcqWIVlctcqGHxdaTcaWGtbWaaSbaaSqa % aiaadchadaWgaaadbaGaamyBaaqabaaaleqaaaGccaGLOaGaayzkaa % aaaa!499E! $$ V\left( {S_{p_1 } \times S_{p_2 } \times \cdots \times S_{p_m } } \right)$$ ....Pages 209-223
Cellular Subrings of the Symmetric Square of a Cellular Ring of Rank 3....Pages 225-249
The Intersection Numbers of the Hecke Algebras H ( PGL n ( q ), BW j B )....Pages 251-263
Ranks and Subdegrees of the Symmetric Groups Acting on Partitions....Pages 265-273
Computation of Lengths of Orbits of a Subgroup in a Transitive Permutation Group....Pages 275-282
Distance-Transitive Graphs and Their Classification....Pages 283-378
On Some Local Characteristics of Distance-Transitive Graphs....Pages 379-394
Action of the Group M 12 on Hadamard Matrices....Pages 395-408
Construction of an Automorphic Graph on 280 Vertices Using Finite Geometries....Pages 409-415
Applications of Group Amalgams to Algebraic Graph Theory....Pages 417-441
A Geometric Characterization of the Group M 22 ....Pages 443-457
Bi-Primitive Cubic Graphs....Pages 459-472
On Some Properties of Geometries of Chevalley Groups and Their Generalizations....Pages 473-505
Back Matter....Pages 507-510

✦ Subjects

Combinatorics; Group Theory and Generalizations