Off-diagonally symmetric domino tilings of the Aztec diamond of odd
order
Off-diagonally symmetric domino tilings of the Aztec diamond of odd
order
We study the enumeration of off-diagonally symmetric domino tilings of odd-order Aztec diamonds in two directions: (1) with one boundary defect, and (2) with maximally-many zeroes on the diagonal. In the first direction, we prove a symmetry property which states that the numbers of off-diagonally symmetric domino tilings of the …