Aztec Diamonds and Baxter Permutations

Details Aztec Diamonds and Baxter Permutations Aztec Diamonds and Baxter Permutations

2003-09-07

arxiv.org/abs/math/0309135v2

The Electronic Journal of Combinatorics 17 (2010), #R105

Mathematics

Combinatorics

12 pages

Scientific paper

We present a proof of a conjecture about the relationship between Baxter permutations and pairs of alternating sign matrices that are produced from domino tilings of Aztec diamonds. It is shown that if and only if a tiling corresponds to a pair of ASMs that are both permutation matrices, the larger permutation matrix corresponds to a Baxter permutation. There has been a thriving literature on both pattern-avoiding permutations of various kinds and tilings of regions using dominos or rhombuses as tiles. However, there have not as of yet been many links between these two areas of enumerative combinatorics. This paper gives one such link.

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