This collection of tutorial and research papers introduces readers to diverse areas of modern pure and applied algebraic combinatorics and finite geometries with a special emphasis on algorithmic aspects and the use of the theory of Gröbner bases.
Topics covered include coherent configurations, association schemes, permutation groups, Latin squares, the Jacobian conjecture, mathematical chemistry, extremal combinatorics, coding theory, designs, etc. Special attention is paid to the description of innovative practical algorithms and their implementation in software packages such as GAP and MAGMA.
Readers will benefit from the exceptional combination of instructive training goals with the presentation of significant new scientific results of an interdisciplinary nature.
Author(s): Aiso Heinze, Mikhail Klin (auth.), Mikhail Klin, Gareth A. Jones, Aleksandar Jurišić, Mikhail Muzychuk, Ilia Ponomarenko (eds.)
Edition: 1
Publisher: Springer-Verlag Berlin Heidelberg
Year: 2009
Language: English
Pages: 311
Tags: Combinatorics; Geometry; Computational Science and Engineering; Mathematics of Computing; Algebra
Front Matter....Pages I-XII
Front Matter....Pages 1-1
Loops, Latin Squares and Strongly Regular Graphs: An Algorithmic Approach via Algebraic Combinatorics....Pages 3-65
Siamese Combinatorial Objects via Computer Algebra Experimentation....Pages 67-112
Using Gröbner Bases to Investigate Flag Algebras and Association Scheme Fusion....Pages 113-135
Enumerating Set Orbits....Pages 137-150
The 2-dimensional Jacobian Conjecture: A Computational Approach....Pages 151-203
Front Matter....Pages 205-205
Some Meeting Points of Gröbner Bases and Combinatorics....Pages 207-227
A Construction of Isomorphism Classes of Oriented Matroids....Pages 229-249
Algorithmic Approach to Non-symmetric 3-class Association Schemes....Pages 251-268
Sets of Type ( d 1 , d 2 ) in Projective Hjelmslev Planes over Galois Rings....Pages 269-278
A Construction of Designs from PSL (2, q ) and PGL (2, q ), q =1 mod 6, on q +2 Points....Pages 279-284
Approaching Some Problems in Finite Geometry Through Algebraic Geometry....Pages 285-296
Computer Aided Investigation of Total Graph Coherent Configurations for Two Infinite Families of Classical Strongly Regular Graphs....Pages 297-311
