Quadratic residues and domino tilings

Authors: Yuhi Kamio, Junnosuke Koizumi, Toshihiko Nakazawa

9 pages. Comments welcome!

Abstract: The formula for the number of domino tilings due to Kasteleyn and Temperley-Fisher is strikingly similar to Eisenstein's formula for the Legendre symbol. We study the connection between these two concepts and prove a formula which expresses the Jacobi symbol in terms of domino tilings.

Submitted to arXiv on 22 Nov. 2023

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