Combinatorial Reductions for the Stanley Depth of I and S/I

Journal Article · Thu Sep 07 04:00:00 EDT 2017 · The Electronic Journal of Combinatorics, 24(3):Article No. P3.48

OSTI ID:1390429

Keller, Mitchel T.; Young, Stephen J.

We develop combinatorial tools to study the realtionship between the Stanley depth of a monomial ideal I and the Stanley depth of its compliment S/I. Using these results we prove that if S is a polynomial ring with at most 5 indeterminates and I is a square-free monomial ideal, then the Stanley depth of I is strictly larger than the Stanley depth of S/I. Using a computer search, we extend the strict inequality to the case of polynomial rings with at most 7 indeterminates. This partially answers questinos asked by Proescu and Qureshi as well as Herzog.

• Research Organization: Pacific Northwest National Laboratory (PNNL), Richland, WA (US)
• Sponsoring Organization: USDOE
• DOE Contract Number: AC05-76RL01830
• OSTI ID: 1390429
• Report Number(s): PNNL-SA-121188
• Journal Information: The Electronic Journal of Combinatorics, 24(3):Article No. P3.48, Journal Name: The Electronic Journal of Combinatorics, 24(3):Article No. P3.48 Journal Issue: 3 Vol. 24; ISSN 1077-8926
• Country of Publication: United States
• Language: English