Enumeration of Alternating Sign Matrices of Even Size (Quasi-)Invariant under a Quarter-Turn Rotation

Jean-Christophe Aval, Philippe Duchon

Abstract


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.


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