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Main Author: Lee, Yi-Lin
Format: Preprint
Published: 2023
Subjects:
Online Access:https://arxiv.org/abs/2303.02750
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author Lee, Yi-Lin
author_facet Lee, Yi-Lin
contents 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.
format Preprint
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institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Off-diagonally symmetric domino tilings of the Aztec diamond
Lee, Yi-Lin
Combinatorics
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.
title Off-diagonally symmetric domino tilings of the Aztec diamond
topic Combinatorics
url https://arxiv.org/abs/2303.02750