Geodesic
Off-diagonally symmetric domino tilings of the Aztec diamond
Yi-Lin Lee1
1Indiana University at Bloomington
The electronic journal of combinatorics, Tome 30 (2023) no. 4
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We introduce a new symmetry class of domino tilings of the Aztec diamond, called the off-diagonal symmetry class, which is motivated by the off-diagonally symmetric alternating sign matrices introduced by Kuperberg in 2002. We use the method of non-intersecting lattice paths and a modification of Stembridge's Pfaffian formula for families of non-intersecting lattice paths to enumerate our new symmetry class. The number of off-diagonally symmetric domino tilings of the Aztec diamond can be expressed as a Pfaffian of a matrix whose entries satisfy a nice and simple recurrence relation.
DOI : 10.37236/11921
Classification : 05A15, 05B20, 05B45
Mots-clés : Stembridge's Pfaffian formula, non-intersecting lattice paths

Yi-Lin Lee  1

1 Indiana University at Bloomington 
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     author = {Yi-Lin Lee},
     title = {Off-diagonally symmetric domino tilings of the {Aztec} diamond},
     journal = {The electronic journal of combinatorics},
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     volume = {30},
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     doi = {10.37236/11921},
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Yi-Lin Lee. Off-diagonally symmetric domino tilings of the Aztec diamond. The electronic journal of combinatorics, Tome 30 (2023) no. 4. doi: 10.37236/11921

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