Algorithmic Algebraic Combinatorics and Gröbner Bases

This collection of tutorial and research papers introduces readers to diverse areas of modern pure and applied algebraic combinatorics and finite geometries. There is special emphasis on algorithmic aspects and the use of the theory of Gröbner bases.

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.

Includes supplementary material: sn.pub/extras

Autorentext

Mikhail Klin graduated from Kiev State University. He has taught future engineers, chemists, teachers of mathematics, and programmers in Ukraine and Russia, serving as a Senior Research Associate in the USSR Academy of Sciences N.D.Zelinskii Institute of Organic Chemistry. Since 1992 he has lived in Israel, visiting universities in the USA, Germany and Fiji. He works in areas of algebraic combinatorics, computer algebra
and permutation group theory, and is coauthor of a textbook and co-editor of several collections of papers.

Gareth Jones graduated from Oxford University, and has spent his career at Southampton University where he is a professor of mathematics. He is co-author of three textbooks, and has published over 60 papers, mainly on group theory and its applications to combinatorics, Galois theory, topology, physics and chemistry.

Aleksandar Jurisic received Ph.D. from the University of Waterloo in '95 in the field of algebraic combinatorics. He teaches mathematics, cryptography and computer security
at the Faculty of Computer and Informatic Science, the University of Ljubljana. His main research interests are discrete mathematics and geometry. In 2005 he co-founded the Slovenian Society of Cryptology.

Mikhail Muzychuk got his Ph.D. from Kiev State University in 1988. In 1991 he moved to Israel. Since then he has been teaching mathematical courses for students of different specialities. Nowadays he is a professor at Netanya Academic College. His main research areas are algebraic combinatorics and group theory. He had published 60
papers in these areas and edited two collections of papers.

Ilya Ponomarenko graduated from the St.Petersburg (Leningrad) State University in 1979 with a degree in Operations Research. After working for 11 years as a
programmer, he worked as a researcher (now leading researcher) in the V.A.Steklov Institute of Mathematics at St.Petersburg, Russian Academy of Sciences, Laboratory of Representation Theory and Computational Methods. In 1986 he obtained his PhD, working on polynomial-time isomorphism testing for graphs, and in 2006 his Dr.Sci., on automorphism groups of association schemes. He is interested in algebraic combinatorics (coherent configurations and permutation groups) and computational complexity (especially the Graph Isomorphism Problem). He has over 50 papers published in refereed mathematical journals.

Inhalt
Tutorials.- Loops, Latin Squares and Strongly Regular Graphs: An Algorithmic Approach via Algebraic Combinatorics.- Siamese Combinatorial Objects via Computer Algebra Experimentation.- Using Gröbner Bases to Investigate Flag Algebras and Association Scheme Fusion.- Enumerating Set Orbits.- The 2-dimensional Jacobian Conjecture: A Computational Approach.- Research Papers.- Some Meeting Points of Gröbner Bases and Combinatorics.- A Construction of Isomorphism Classes of Oriented Matroids.- Algorithmic Approach to Non-symmetric 3-class Association Schemes.- Sets of Type (d 1,d 2) in Projective Hjelmslev Planes over Galois Rings.- A Construction of Designs from PSL(2,q) and PGL(2,q), q=1 mod 6, on q+2 Points.- Approaching Some Problems in Finite Geometry Through Algebraic Geometry.- Computer Aided Investigation of Total Graph Coherent Configurations for Two Infinite Families of Classical Strongly Regular Graphs.