A poset ${\Phi }_n$ whose maximal chains are in bijection with the $n\times n$ alternating sign matrices

Abstract

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

6 pages