Algorithmic Algebraic Combinatorics and Gröbner Bases
Klin, M., Jones, G.A., Jurisic, A., Muzychuk, M., Ponomarenko, I. (Eds.)
2009, XII, 311p.
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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.
Content Level »Research
Keywords »Algebra - Area - Computer - Graph - Gröbner bases - Permutation - algorithms - association scheme - coding theory - computer algebra - construction - finite geometry
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.