Geodesic
A large dihedral symmetry of the set of alternating sign matrices
The electronic journal of combinatorics, Tome 7 (2000)
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We prove a conjecture of Cohn and Propp, which refines a conjecture of Bosley and Fidkowski about the symmetry of the set of alternating sign matrices (ASMs). We examine data arising from the representation of an ASM as a collection of paths connecting $2n$ vertices and show it to be invariant under the dihedral group $D_{2n}$ rearranging those vertices, which is much bigger than the group of symmetries of the square. We also generalize conjectures of Propp and Wilson relating some of this data for different values of $n$.
DOI : 10.37236/1515
Classification : 05A19, 52C20, 82B20
Mots-clés : alternating sign matrices, square lattice 
@article{10_37236_1515,
     author = {Benjamin Wieland},
     title = {A large dihedral symmetry of the set of alternating sign matrices},
     journal = {The electronic journal of combinatorics},
     year = {2000},
     volume = {7},
     doi = {10.37236/1515},
     zbl = {0956.05015},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1515/}
}
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Benjamin Wieland. A large dihedral symmetry of the set of alternating sign matrices. The electronic journal of combinatorics, Tome 7 (2000). doi: 10.37236/1515

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