2024/10/30 by Paul, Pravakar, Saikia, Manjil P.
#05C70 #52C20 #68R10 #Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Primary 05C30 #Secondary 05A15
paper · doi:10.48550/arxiv.2410.23324
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.