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Tetromino tilings and the Tutte polynomial

Jesper Lykke Jacobsen
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Abstract

We consider tiling rectangles of size 4m x 4n by T-shaped tetrominoes. Each tile is assigned a weight that depends on its orientation and position on the lattice. For a particular choice of the weights, the generating function of tilings is shown to be the evaluation of the multivariate Tutte polynomial Z\_G(Q,v) (known also to physicists as the partition function of the Q-state Potts model) on an (m-1) x (n-1) rectangle G, where the parameter Q and the edge weights v can take arbitrary values depending on the tile weights.

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Jesper Lykke Jacobsen. 2006-09-19. Tetromino tilings and the Tutte polynomial. https://doi.org/10.1088/1751-8113%2F40%2F7%2F002

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