The lex game and some applications

• Autores: Lajos Rónyai, Balázs Ráth, Bálint Felszeghy
• Localización: Journal of symbolic computation, ISSN 0747-7171, Vol. 41, Nº 6, 2006, págs. 663-681
• Idioma: inglés
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• Resumen

  • Let be a field, V a finite subset of . We introduce the lex game, which yields a combinatorial description of the lexicographic standard monomials of the ideal I(V) of polynomials vanishing on V.

    As a consequence, we obtain a fast algorithm which computes the lexicographic standard monomials of I(V).

    We apply the lex game to calculate explicitly the standard monomials for special types of subsets of {0,1}n. For let VD denote the vectors in which the number of ones (the Hamming weight of ) is in D. We calculate the lexicographic standard monomials of VD, where for fixed with 0=d