We develop combinatorial tools to study the relationship between the Stanley depth of a monomial ideal $I$ and the Stanley depth of its compliment, $S/I$. Using these results we are able to 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 $S/I$ is strictly larger than the Stanley depth of $I$. Using a computer search, we are able to extend this strict inequality up to polynomial rings with at most 7 indeterminates. This partially answers questions asked by Propescu and Qureshi as well as Herzog.
@article{10_37236_6783,
author = {Mitchel T. Keller and Stephen J. Young},
title = {Combinatorial reductions for the {Stanley} depth of {\(I\)} and {\(S/I\)}},
journal = {The electronic journal of combinatorics},
year = {2017},
volume = {24},
number = {3},
doi = {10.37236/6783},
zbl = {1440.13049},
url = {http://geodesic.mathdoc.fr/articles/10.37236/6783/}
}
TY - JOUR
AU - Mitchel T. Keller
AU - Stephen J. Young
TI - Combinatorial reductions for the Stanley depth of \(I\) and \(S/I\)
JO - The electronic journal of combinatorics
PY - 2017
VL - 24
IS - 3
UR - http://geodesic.mathdoc.fr/articles/10.37236/6783/
DO - 10.37236/6783
ID - 10_37236_6783
ER -
%0 Journal Article
%A Mitchel T. Keller
%A Stephen J. Young
%T Combinatorial reductions for the Stanley depth of \(I\) and \(S/I\)
%J The electronic journal of combinatorics
%D 2017
%V 24
%N 3
%U http://geodesic.mathdoc.fr/articles/10.37236/6783/
%R 10.37236/6783
%F 10_37236_6783
Mitchel T. Keller; Stephen J. Young. Combinatorial reductions for the Stanley depth of \(I\) and \(S/I\). The electronic journal of combinatorics, Tome 24 (2017) no. 3. doi: 10.37236/6783
