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Properties of Commutative Association Schemes derived by FGLM Techniques
Association schemes are combinatorial objects that allow us solve problems in
several branches of mathematics. They have been used in the study of
permutation groups and graphs and also in the design of experiments, coding
theory, partition designs etc. In this paper we show some techniques for
computing properties of association schemes. The main framework arises from the
fact that we can characterize completely the Bose-Mesner algebra in terms of a
zero-dimensional ideal. A Gr\"obner basis of this ideal can be easily derived
without the use of Buchberger algorithm in an efficient way. From this
statement, some nice relations arise between the treatment of zero-dimensional
ideals by reordering techniques (FGLM techniques) and some properties of the
schemes such as P-polynomiality, and minimal generators of the algebra.Comment: 12 pages, to appear in the International Journal of Algebra and
Computatio