Tetromino tilings and the Tutte polynomial

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dc.creatorJacobsen, Jesper Lykke
dc.date2006-09-18
dc.date2006-09-19
dc.date.accessioned2026-07-07T08:26:33Z
dc.date.available2026-07-07T08:26:33Z
dc.descriptionWe 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.
dc.description8 pages, 6 figures
dc.identifierhttps://arxiv.org/abs/math/0609506
dc.identifierhttp://arxiv.org/abs/math/0609506
dc.identifierJournal of Physics A Mathematical and Theoretical 40 (2007) 1439-1446
dc.identifierdoi:10.1088/1751-8113/40/7/002
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/136976
dc.subjectCombinatorics
dc.subjectStatistical Mechanics
dc.subjectMathematical Physics
dc.titleTetromino tilings and the Tutte polynomial
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