Effective poset inequalities
Combinatorics
2023-09-15 v3 Computational Complexity
Discrete Mathematics
Abstract
We explore inequalities on linear extensions of posets and make them effective in different ways. First, we study the Bj\"orner--Wachs inequality and generalize it to inequalities on order polynomials and their -analogues via direct injections and FKG inequalities. Second, we give an injective proof of the Sidorenko inequality with computational complexity significance, namely that the difference is in . Third, we generalize the Sidorenko inequality to posets with small chain intersections and give complexity theoretic applications.
Cite
@article{arxiv.2205.02798,
title = {Effective poset inequalities},
author = {Swee Hong Chan and Igor Pak and Greta Panova},
journal= {arXiv preprint arXiv:2205.02798},
year = {2023}
}
Comments
36 pages, 1 figure. Added a reference to Daykin--Daykin--Paterson inequality that were previously presented as Conjecture 4.19 in v2