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TitleStandard monomials for partitions.
Author(s) Gleb Gusev, Lajos Rónyai
TypeArticle in Journal
AbstractLet F be a field, and α0,...,αk-1 be k distinct elements of F. Let λ =(λ1,...,λk) be a partition of n and V λ be the set of all vectors v=(v 1,...,v n)∈ F n such that |{j ∈ [n] : v j=αi}|=λi+1 for 0≦ i ≦\ k-1. We describe the lexicographic standard monomials of the ideal of polynomials from F[x 1,...,x n] which vanish on the set V λ. In the proof we give a new description of the orthogonal complement (S λ)⊥ (with respect to the James scalar product) of the Specht module S λ. As applications, a basis of (S λ)⊥ is exhibited, and we obtain a combinatorial description of the Hilbert function of V λ.. Our approach gives also the deglex standard monomials of V λ, and hence provides a new proof of a result of A. M. Garsia and C. Procesi [10].
KeywordsGröbner basis, standard monomial, tableau
ISSN0236-5294; 1588-2632/e
URL http://link.springer.com/article/10.1007%2Fs10474-006-0049-1
JournalActa Math. Hung.
PublisherSpringer Netherlands, Dordrecht; Akad
Translation No
Refereed No