Symmetric Domino Tilings of Aztec Diamonds
Pravakar Paul, Manjil P. Saikia
TL;DR
This paper introduces new inductive formulas for counting symmetric domino tilings of Aztec Diamonds, including diagonally symmetric and anti-symmetrically symmetric cases, using a novel graph matching technique.
Contribution
It presents the first inductive sum formulas for symmetric tilings of Aztec Diamonds and extends these to the unrestricted case, employing a new graph counting method.
Findings
Formulas for diagonally symmetric tilings
Formulas for diagonally & anti-diagonally symmetric tilings
Extension to unrestricted tilings
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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsMathematical Dynamics and Fractals · Quasicrystal Structures and Properties