Algorithmic Algebraic Combinatorics and Gröbner Bases

In 2006 a special semester on Gr¿ obner bases and related methods was or- nized by RICAM and RISC, directed by Bruno Buchberger and Heinz Engl. The main focus of the semester were the development of the formal theory of Gr¿ obner bases (brie?y GB), the e?cient implementation of all algorithms related to this theory, and the promotion of recent and new applications of GB. The workshop D1 ¿Gr¿ obner bases in cryptography, coding theory and - gebraic combinatorics¿, Linz, May 1¿6, 2006 (chairmen M. Klin, L. Perret, M. Sala) was one of the main ingredients of the semester. The last two days of this workshop, devoted to combinatorics, made it possible to bring together experts in algorithmic problems related to coherent con?gurations and as- ciation schemes with a community of people working in the area of GB. Each side was interested in understanding the computational problems and current algorithmicpossibilitiesoftheother,withaparticularobjectiveofintroducing the practical use of GB in algebraic combinatorics. Materials (mainly slides of lectures and posters) available from the site ricam.oeaw.ac.at/specsem/srs/groeb/schedule D1.htmlprovidea helpful and vivid picture of the successful exchange of scienti?c information during the workshop D1. Asafollow-uptothespecialsemester,10volumesofproceedingsarebeing published by di?erent publishers. The current collection of papers re?ects diverse investigations in the area of algebraic combinatorics (with or without explicit use of GB), but with a de?nite emphasis on algorithmic approaches.

Includes supplementary material: sn.pub/extras

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.