Almost reverse lexicographic ideals and Fröberg sequence

2009/10/20 by Jung Pil Park, Park, Jung Pil
Computer Science · Mathematics · #Commutative Algebra and Its Applications #Polynomial and algebraic computation #Rings, Modules, and Algebras #math.AC #msc:13A02 #msc:13C05 #msc:13D40 #msc:13E10 #msc:13P10

paper · pdf · doi:10.48550/arxiv.0910.3830

21 pages; Because there is a crutial misunderstanding in the previous version, we modified the article. Thanks Giulio Caviglia for your kindness advise

arxiv created 2009/10/23 · arxiv updated 2009/12/01

Abstract

We study almost reverse lexicographic ideals in a polynomial ring over a field of arbitrary characteristic. We give a criterion for a given sequence of nonnegative integers to be the Hilbert function of an almost reverse lexicographic ideal in the polynomial ring. Then it will be shown that every Fröberg sequence satisfies this criterion.

Related

• Conditions for Generic Initial Ideals to be Almost Reverse Lexicographic
• On almost revlex ideals with Hilbert function of complete intersections
• Reverse Lexicographic and Lexicographic Shifting
• The initial ideal of generic sequences and Fröberg's Conjecture
• The strong Lefschetz property for quadratic reverse lexicographic ideals