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arXiv · 2303.02750

Off-diagonally symmetric domino tilings of the Aztec diamond

Yi-Lin Lee
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Abstract

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.

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Yi-Lin Lee. 2023-03-05. Off-diagonally symmetric domino tilings of the Aztec diamond. https://doi.org/10.37236/11921

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