Dimers, Tilings and Trees

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dc.creatorKenyon, Richard
dc.creatorSheffield, Scott
dc.date2003-10-13
dc.date.accessioned2026-07-07T05:01:52Z
dc.date.available2026-07-07T05:01:52Z
dc.descriptionGeneralizing results of Temperley, Brooks, Smith, Stone and Tutte and others we describe a natural equivalence between three planar objects: weighted bipartite planar graphs; planar Markov chains; and tilings with convex polygons. This equivalence provides a measure-preserving bijection between dimer coverings of a weighted bipartite planar graph and spanning trees on the corresponding Markov chain. The tilings correspond to harmonic functions on the Markov chain and to ``discrete analytic functions'' on the bipartite graph. The equivalence is extended to infinite periodic graphs, and we classify the resulting ``almost periodic'' tilings and harmonic functions.
dc.description23 pages, 5 figures
dc.identifierhttps://arxiv.org/abs/math/0310195
dc.identifierhttp://arxiv.org/abs/math/0310195
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/68840
dc.subjectCombinatorics
dc.subjectMathematical Physics
dc.subjectProbability
dc.titleDimers, Tilings and Trees
dc.typetext

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