Keys and alternating sign matrices

Jean-Christophe Aval (1)

1 LaBRI - Laboratoire Bordelais de Recherche en Informatique

Lascoux and Schützenberger introduced a notion of key associated to any Young tableau. More recently Lascoux defined the key of an alternating sign matrix by recursively removing all -1's in such matrices. But alternating sign matrices are in bijection with monotone triangles, which form a subclass of Young tableaux. We show that in this case these two notions of keys coincide. Moreover we obtain an elegant and direct way to compute the key of any Young tableau, and discuss consequences of our result.

Mots clés: Young tableaux; keys; alternating sign matrices

Domaines: Combinatoire [math.CO]

Jean-Christophe Aval. Keys and alternating sign matrices. Seminaire Lotharingien de Combinatoire, 2008, 59, pp.B59f. ⟨hal-00187263v2⟩