The lex game and some applications

Bálint Felszeghy, Balázs Ráth, Lajos Rónyai

Research output: Contribution to journalArticle

27 Citations (Scopus)

Abstract

Let F be a field, V a finite subset of Fn. 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 D â Z let VD denote the vectors y â { 0, 1 }n in which the number of ones (the Hamming weight of y) is in D. We calculate the lexicographic standard monomials of VD, where {A formula is presented} for d, â, r â N fixed with 0 â d < r and 0 < â < r. This extends the results of [Anstee, R.P., Rónyai, L., Sali, A., 2002. Shattering news. Graphs and Combinatorics 18, 59-73, Friedl, K., Hegedu{combining double acute accent}s, G., Rónyai, L., Gröbner bases for complete l-wide families (in press) and Hegedu{combining double acute accent}s, G., Rónyai, L., 2003. Gröbner bases for complete uniform families. Journal of Algebraic Combinatorics 17, 171-180].

Original languageEnglish
Pages (from-to)663-681
Number of pages19
JournalJournal of Symbolic Computation
Volume41
Issue number6
DOIs
Publication statusPublished - Jun 1 2006

Keywords

  • Combinatorial algorithm
  • Gröbner basis
  • Standard monomials

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Computational Mathematics

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