English

Symmetric Domino Tilings of Aztec Diamonds

Combinatorics 2024-11-01 v1 Discrete Mathematics

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.

Keywords

Cite

@article{arxiv.2410.23324,
  title  = {Symmetric Domino Tilings of Aztec Diamonds},
  author = {Pravakar Paul and Manjil P. Saikia},
  journal= {arXiv preprint arXiv:2410.23324},
  year   = {2024}
}

Comments

19 pages, 11 figures, 3 tables, comments are welcome