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Acta Mathematica Vietnamica

Lexsegment Ideals and Their h-Polynomials

Takayuki Hibi , icon-email Kazunori Matsuda

Abstract

Let S=K[x1,,xn] denote the polynomial ring in n variables over a field K with each degxi=1 and IS a homogeneous ideal of S with dimS/I=d. The Hilbert series of S/I is of the form hS/I(λ)/(1λ)d, where hS/I(λ)=h0+h1λ+h2λ2++hsλs with hs0 is the h-polynomial of S/I. Given arbitrary integers r1 and s1, a lexsegment ideal I of S=K[x1,,xn], where nmax{r,s}+2, satisfying reg(S/I)=r and deghS/I(λ)=s will be constructed.