Betti numbers of lex ideals over some Macaulay-Lex rings

Jeff Mermin, Satoshi Murai*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)


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
Issue number2
Publication statusPublished - 2010 Mar
Externally publishedYes


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

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Discrete Mathematics and Combinatorics


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