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

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 unrestrited ASm's and the number of half-turn symmetric ASM's.
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https://hal.inria.fr/hal-00369501
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Jean-Christophe Aval, Philippe Duchon. Enumeration of alternating sign matrices of even size (quasi)-invariant under a quarter-turn rotation. 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009), 2009, Hagenberg, Austria. pp.115-126. ⟨hal-00369501⟩

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