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Enumeration of alternating sign matrices of even size (quasi)-invariant under a quarter-turn rotation
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AK, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009), DMTCS Proceedings vol. AK, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009) (2009).

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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. 
@article{DMTCS_2009_special_256_a48,
     author = {Aval, Jean-Christophe and Duchon, Philippe},
     title = {Enumeration of alternating sign matrices of even size (quasi)-invariant under a quarter-turn rotation},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings vol. AK, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009)},
     year = {2009},
     doi = {10.46298/dmtcs.2726},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2726/}
}
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Aval, Jean-Christophe; Duchon, Philippe. Enumeration of alternating sign matrices of even size (quasi)-invariant under a quarter-turn rotation. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AK, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009), DMTCS Proceedings vol. AK, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009) (2009). doi : 10.46298/dmtcs.2726. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2726/

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