A poset $\Phi_n$ whose maximal chains are in bijection with the $n \times n$ alternating sign matrices

Paul Terwilliger

A poset $\Phi_n$ whose maximal chains are in bijection with the $n \times n$ alternating sign matrices

Combinatorics 2017-10-16 v1

Authors: Paul Terwilliger

Abstract

For an integer $n\geq 1$ , we display a poset $\Phi_n$ whose maximal chains are in bijection with the $n\times n$ alternating sign matrices. The Hasse diagram $\widehat \Phi_n$ is obtained from the $n$ -cube by adding some edges. We show that the dihedral group $D_{2n}$ acts on $\widehat \Phi_n$ as a group of automorphisms.

Keywords

weakly reversible mass-action systems positive steady state stoichiometric class chemical reaction network

Cite

@article{arxiv.1710.04733,
  title  = {A poset $\Phi_n$ whose maximal chains are in bijection with the $n \times n$ alternating sign matrices},
  author = {Paul Terwilliger},
  journal= {arXiv preprint arXiv:1710.04733},
  year   = {2017}
}

Comments

6 pages

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