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Symmetric Domino Tilings of Aztec Diamonds

Published 30 Oct 2024 in math.CO and cs.DM | (2410.23324v1)

Abstract: In this paper, we give inductive sum formulas to calculate the number of diagonally symmetric, and diagonally & anti-diagonally symmetric domino tilings of Aztec Diamonds. As a byproduct, we also find such a formula for the unrestricted case as well. Our proofs rely on a new technique for counting the number of perfect matchings of graphs, proposed by the authors recently.

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