Séminaire Combinatoire et Théorie des Nombres ICJ

Distributive Lattice of Half-Turn Symmetric Alternating Sign Matrices

by Masao Ishikawa

Europe/Paris
Bât. Braconnier, salle Fokko du Cloux (ICJ, Université Lyon 1)

Bât. Braconnier, salle Fokko du Cloux

ICJ, Université Lyon 1

Description

Striker and Williams defined promotion and rowmotion for the toggle group of an rc-poset.
They investigated the distributive lattice of the alternating sign matrices which is the lattice of order ideals of the poset $\bf{A}_n$, which is obtained by gluing the positive root posets $\Phi^+(A_k)$.
We consider the set of the half-turn symmetric alternating sign matrices as a distributive lattice by the height function and investigate the underlying poset, which is obtained by gluing the positive root posets $\Phi^+(B_k)$.