Stirling Posets
Combinatorics
2018-06-12 v2 Algebraic Geometry
Abstract
We define combinatorially a partial order on the set partitions and show that it is equivalent to the Bruhat-Chevalley-Renner order on the upper triangular matrices. By considering subposets consisting of set partitions with a fixed number of blocks, we introduce and investigate "Stirling posets." As we show, the Stirling posets have a hierarchy and they glue together to give the whole set partition poset. Moreover, we show that they (Stirling posets) are graded and EL-shellable. We offer various reformulations of their length functions and determine the recurrences for their length generating series.
Cite
@article{arxiv.1801.08231,
title = {Stirling Posets},
author = {Mahir Bilen Can and Yonah Cherniavsky},
journal= {arXiv preprint arXiv:1801.08231},
year = {2018}
}
Comments
New references are added, several typos are fixed