Algorithmic Algebraic Combinatorics and Grbner Bases [Paperback]

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 Gr?bner bases.

Tutorials.- Loops, Latin Squares and Strongly Regular Graphs: An Algorithmic Approach via?Algebraic Combinatorics.- Siamese Combinatorial Objects via Computer Algebra Experimentation.- Using Gr?bner 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 Gr?bner 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.

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 appl³“