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

Abstract

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.

Authors:
;
Publication Date:
Research Org.:
Pacific Northwest National Lab. (PNNL), Richland, WA (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1390429
Report Number(s):
PNNL-SA-121188
Journal ID: ISSN 1077-8926
DOE Contract Number:  
AC05-76RL01830
Resource Type:
Journal Article
Journal Name:
The Electronic Journal of Combinatorics, 24(3):Article No. P3.48
Additional Journal Information:
Journal Volume: 24; Journal Issue: 3; Journal ID: ISSN 1077-8926
Country of Publication:
United States
Language:
English

Citation Formats

Keller, Mitchel T., and Young, Stephen J. Combinatorial Reductions for the Stanley Depth of I and S/I. United States: N. p., 2017. Web.
Keller, Mitchel T., & Young, Stephen J. Combinatorial Reductions for the Stanley Depth of I and S/I. United States.
Keller, Mitchel T., and Young, Stephen J. Thu . "Combinatorial Reductions for the Stanley Depth of I and S/I". United States.
@article{osti_1390429,
title = {Combinatorial Reductions for the Stanley Depth of I and S/I},
author = {Keller, Mitchel T. and Young, Stephen J.},
abstractNote = {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.},
doi = {},
journal = {The Electronic Journal of Combinatorics, 24(3):Article No. P3.48},
issn = {1077-8926},
number = 3,
volume = 24,
place = {United States},
year = {2017},
month = {9}
}