Posets of width two and skew Young diagrams

Richard P. Stanley

Posets of width two and skew Young diagrams

Combinatorics 2023-05-05 v2

Authors: Richard P. Stanley

Abstract

Let $P$ be a finite poset of width two, i.e., with no three-element antichain. We associate with $P$ a skew Young diagram $\Upsilon(P)$ and discuss some of the properties of the map $\Upsilon$ . In particular, if we regard $\Upsilon(P)$ as a poset in a standard way, then the linear extensions of $P$ are in bijection with the order ideals of $\Upsilon(P)$ .

Keywords

finite poset width two skew young diagram linear extension order ideal antichain

Cite

@article{arxiv.2304.13112,
  title  = {Posets of width two and skew Young diagrams},
  author = {Richard P. Stanley},
  journal= {arXiv preprint arXiv:2304.13112},
  year   = {2023}
}

Comments

Several people pointed out that most of my results had already been published elsewhere

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