Enumeration of alternating sign matrices of even size (quasi-)nvariant under a quarter-turn rotation

Jean-Christophe Aval (1) , Philippe Duchon (1)

1 LaBRI - Laboratoire Bordelais de Recherche en Informatique

The aim of this work is to enumerate alternating sign matrices (ASM) that are quasi-invariant under a quarter-turn. The enumeration formula (conjectured by Duchon) involves, as a product of three terms, the number of unrestricted ASM's and the number of half-turn symmetric ASM's.

Mots clés: alternating sign matrices; square ice models

Domaines: Combinatoire [math.CO]

Jean-Christophe Aval, Philippe Duchon. Enumeration of alternating sign matrices of even size (quasi-)nvariant under a quarter-turn rotation. The Electronic Journal of Combinatorics, 2010, 17, pp.R51. ⟨hal-00424488⟩