Extensions of the Kahn--Saks inequality for posets of width two
Combinatorics
2023-05-11 v3
Abstract
The Kahn--Saks inequality is a classical result on the number of linear extensions of finite posets. We give a new proof of this inequality for posets of width two using explicit injections of lattice paths. As a consequence we obtain a -analogue, a multivariate generalization and an equality condition in this case. We also discuss the equality conditions of the Kahn--Saks inequality for general posets and prove several implications between conditions conjectured to be equivalent.
Keywords
Cite
@article{arxiv.2106.07133,
title = {Extensions of the Kahn--Saks inequality for posets of width two},
author = {Swee Hong Chan and Igor Pak and Greta Panova},
journal= {arXiv preprint arXiv:2106.07133},
year = {2023}
}
Comments
25 pages; v3: added conditions to Theorem 1.4 and 1.6, revised Conjecture in Section 8, added example 1.5