Off-diagonally symmetric domino tilings of the Aztec diamond
arXiv:2303.02750 · doi:10.37236/11921
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.
24 pages, 9 figures, comments are welcome. To appear in the Electronic Journal of Combinatorics