これに証明載ってるかも
https://inis.iaea.org/collection/NCLCollectionStore/_Public/38/098/38098203.pdf?r=1&;r=1

Section2
A famous result of Kasteleyn [8] and Temperley and Fisher [18] counts the
number of domino tilings of a chessboard (or any other rectangular region).
In this section we explain Kasteleyn's proof.


「ドミノによるタイル張り」(京大･理)　36p.
http://www.ms.u-tokyo.ac.jp/~kazushi/proceedings/domino.pdf

「長方形領域のドミノタイル張りについて」(青学大･理工)　17p.
http://www.gem.aoyama.ac.jp/~kyo/sotsuken/2010/fujino_sotsuron_2010.pdf