Abstract
We consider tiling rectangles of size 4m × 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 ZG(Q, v) (known also to physicists as the partition function of the Q-state Potts model) on an (m − 1) × (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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