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.
Revised: February 12, 2021 |
Published: September 7, 2017
Citation
Keller M.T., and S.J. Young. 2017.Combinatorial Reductions for the Stanley Depth of I and S/I.The Electronic Journal of Combinatorics 24, no. 3:Article No. P3.48.PNNL-SA-121188.