Off-diagonally symmetric domino tilings of the Aztec diamond (Q6117238)

Summary: 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 \textit{G. Kuperberg} in [Ann. Math. (2) 156, No. 3, 835--866 (2002; Zbl 1010.05014)]. 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.