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Domino tilings of
Aztec diamonds, Baxter permutations, and snow leopard
permutations
Benjamin Caffrey, Eric S. Egge, Gregory Michel, Kailee Rubin and Jonathan Ver Steegh
Vol. 8 (2015), No. 5, 833–858
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Abstract |
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In 1992, Elkies, Kuperberg, Larsen, and Propp introduced a bijection between domino tilings of Aztec diamonds and certain pairs of alternating-sign matrices whose sizes differ by one. In this paper we first study those smaller permutations which, when viewed as matrices, are paired with the matrices for doubly alternating Baxter permutations. We call these permutations snow leopard permutations, and we use a recursive decomposition to show they are counted by the Catalan numbers. This decomposition induces a natural map from Catalan paths to snow leopard permutations; we give a simple combinatorial description of the inverse of this map. Finally, we also give a set of transpositions which generates these permutations. |
Keywords
domino tiling, Aztec diamond, Baxter permutation,
alternating permutation, alternating-sign matrix, Catalan
number
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Mathematical Subject Classification 2010
Primary: 05A05, 05A15
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Milestones
Received: 28 April 2014
Revised: 5 December 2014
Accepted: 8 December 2014
Published: 28 September 2015
Communicated by Arthur T. Benjamin
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Authors |
| Benjamin Caffrey | |
| Epic 1979 Milky Way Verona, WI 53593 United States |
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| Eric S. Egge | |
| Department of Mathematics and
Statistics Carleton College Northfield, MN 55057 United States |
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| Gregory Michel | |
| Department of Mathematics University of Minnesota Twin Cities Minneapolis, MN 55455 United States |
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| Kailee Rubin | |
| Epic 1979 Milky Way Verona, WI 53593 United States |
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| Jonathan Ver Steegh | |
| Carleton College Northfield, MN 55057 United States |
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