Journal of Algebraic Combinatorics

, Volume 33, Issue 2, pp 313–324

On the Stanley depth of squarefree Veronese ideals


    • School of MathematicsGeorgia Institute of Technology
  • Yi-Huang Shen
    • Department of MathematicsUniversity of Science and Technology of China
  • Noah Streib
    • School of MathematicsGeorgia Institute of Technology
  • Stephen J. Young
    • School of MathematicsGeorgia Institute of Technology
    • Department of MathematicsUniversity of California, San Diego
Open AccessArticle

DOI: 10.1007/s10801-010-0249-1

Cite this article as:
Keller, M.T., Shen, Y., Streib, N. et al. J Algebr Comb (2011) 33: 313. doi:10.1007/s10801-010-0249-1


Let K be a field and S=K[x 1,…,x n ]. In 1982, Stanley defined what is now called the Stanley depth of an S-module M, denoted sdepth (M), and conjectured that depth (M)≤sdepth (M) for all finitely generated S-modules M. This conjecture remains open for most cases. However, Herzog, Vladoiu and Zheng recently proposed a method of attack in the case when M=I/J with JI being monomial S-ideals. Specifically, their method associates M with a partially ordered set. In this paper we take advantage of this association by using combinatorial tools to analyze squarefree Veronese ideals in S. In particular, if I n,d is the squarefree Veronese ideal generated by all squarefree monomials of degree d, we show that if 1≤dn<5d+4, then sdepth (I n,d)=⌊(nd)/(d+1)⌋+d, and if d≥1 and n≥5d+4, then d+3≤sdepth (I n,d)≤⌊(nd)/(d+1)⌋+d.


Stanley depth Squarefree monomial ideal Interval partition Squarefree Veronese ideal

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© The Author(s) 2010