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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 theoff-diagonally symmetric alternating sign matrices introduced by Kuperberg in2002. We use the method of non-intersecting lattice paths and a modification ofStembridge's Pfaffian formula for families of non-intersecting lattice paths toenumerate our new symmetry class. The number of off-diagonally symmetric dominotilings of the Aztec diamond can be expressed as a Pfaffian of a matrix whoseentries satisfy a nice and simple recurrence relation.

Off-diagonally symmetric domino tilings of the Aztec diamond