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COMBINATORICS
2000

Large Dihedral Symmetry of the Set of Alternating Sign Matrices

13 years 11 months ago
Large Dihedral Symmetry of the Set of Alternating Sign Matrices
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 D2n 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. AMS Subect Classification (2000): Primary 05A19; Secondary 52C20, 82B20.
Benjamin Wieland
Added 17 Dec 2010
Updated 17 Dec 2010
Type Journal
Year 2000
Where COMBINATORICS
Authors Benjamin Wieland
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