Vol. 8, No. 5, 2015

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ISSN: 1944-4184 (e-only)
ISSN: 1944-4176 (print)
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
Abstract

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
Mathematical Subject Classification 2010
Primary: 05A05, 05A15
Milestones
Received: 28 April 2014
Revised: 5 December 2014
Accepted: 8 December 2014
Published: 28 September 2015

Communicated by Arthur T. Benjamin
Authors
Benjamin Caffrey
Epic
1979 Milky Way
Verona, WI 53593
United States
Eric S. Egge
Department of Mathematics and Statistics
Carleton College
Northfield, MN 55057
United States
Gregory Michel
Department of Mathematics
University of Minnesota Twin Cities
Minneapolis, MN 55455
United States
Kailee Rubin
Epic
1979 Milky Way Verona, WI 53593
United States
Jonathan Ver Steegh
Carleton College
Northfield, MN 55057
United States