Lexsegment ideals and their h-polynomials

2018/07/08 by Takayuki Hibi, Hibi, Takayuki, Kazunori Matsuda +1
Mathematics · Computer Science · #Commutative Algebra and Its Applications #Polynomial and algebraic computation #Algebraic Geometry and Number Theory

paper · pdf · doi:10.48550/arxiv.1807.02834

Abstract

Let S = K[x₁, …, x_n] denote the polynomial ring in n variables over a field K with each deg x_i = 1 and I ⊂ S a homogeneous ideal of S with dim S/I = d. The Hilbert series of S/I is of the form h_S/I(λ)/(1 - λ)^d, where h_S/I(λ) = h₀ + h₁λ+ h₂λ² + ⋯ + h_sλ^s with h_s ≠ 0 is the h-polynomial of S/I. Given arbitrary integers r ≥ 1 and s ≥ 1, a lexsegment ideal I of S = K[x₁, …, x_n], where n ≤ max\r, s\ + 2, satisfying reg(S/I) = r and deg h_S/I(λ) = s will be constructed.

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