Geodesic
Aztec diamonds and Baxter permutations
The electronic journal of combinatorics, Tome 17 (2010)

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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 a tiling corresponds to a pair of ASMs that are both permutation matrices if and only if the larger permutation matrix corresponds to a Baxter permutation. There has been a thriving literature on both pattern-avoiding permutations of various kinds [Baxter 1964, Dulucq and Guibert 1988] and tilings of regions using dominos or rhombuses as tiles [Elkies et al. 1992, Kuo 2004]. However, there have not as of yet been many links between these two areas of enumerative combinatorics. This paper gives one such link.
DOI : 10.37236/377
Classification : 52C20, 05A19
Mots-clés : Baxter permutation, alternating sign matrices, domino tiling, Aztec diamonds 
Hal Canary. Aztec diamonds and Baxter permutations. The electronic journal of combinatorics, Tome 17 (2010). doi: 10.37236/377
@article{10_37236_377,
     author = {Hal Canary},
     title = {Aztec diamonds and {Baxter} permutations},
     journal = {The electronic journal of combinatorics},
     year = {2010},
     volume = {17},
     doi = {10.37236/377},
     zbl = {1201.52019},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/377/}
}
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