Distributive Lattice of Half-Turn Symmetric Alternating Sign Matrices

par Masao Ishikawa

mardi 10 sept. 2019, 10:45 → 11:45 Europe/Paris

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

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 $\Phi^+(B_k)$.