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  • Author or Editor: Lajos Rónyai x
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Let 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 ji}|=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].

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