Betti numbers of lex ideals over some Macaulay-Lex rings

Jeff Mermin, Satoshi Murai

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

Let A = K [x1,.,xn] be a polynomial ring over a field K and M a monomial ideal of A. The quotient ring R = A/M is said to be Macaulay-Lex if every Hilbert function of a homogeneous ideal of R is attained by a lex ideal. In this paper, we introduce some new Macaulay-Lex rings and study the Betti numbers of lex ideals of those rings. In particular, we prove a refinement of the Frankl-Füredi-Kalai Theorem which characterizes the face vectors of colored complexes. Additionally, we disprove a conjecture of Mermin and Peeva that lex-plus-M ideals have maximal Betti numbers when A/M is Macaulay-Lex.

Original languageEnglish
Pages (from-to)299-318
Number of pages20
JournalJournal of Algebraic Combinatorics
Volume31
Issue number2
DOIs
Publication statusPublished - 2010 Mar 1
Externally publishedYes

Fingerprint

Betti numbers
Ring
M-ideal
Monomial Ideals
Quotient ring
Hilbert Function
Disprove
Polynomial ring
Refinement
Face
Theorem

Keywords

  • Colored simplicial complexes
  • Graded Betti numbers
  • Hilbert functions
  • Lex ideals

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Discrete Mathematics and Combinatorics

Cite this

Betti numbers of lex ideals over some Macaulay-Lex rings. / Mermin, Jeff; Murai, Satoshi.

In: Journal of Algebraic Combinatorics, Vol. 31, No. 2, 01.03.2010, p. 299-318.

Research output: Contribution to journalArticle

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