Singular polynomials of generalized Kasteleyn matrices

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dc.creatorSaldanha, Nicolau C.
dc.date2000-12-30
dc.date.accessioned2026-07-07T04:39:27Z
dc.date.available2026-07-07T04:39:27Z
dc.descriptionKasteleyn counted the number of domino tilings of a rectangle by considering a mutation of the adjacency matrix: a Kasteleyn matrix K. In this paper we present a generalization of Kasteleyn matrices and a combinatorial interpretation for the coefficients of the characteristic polynomial of KK^\ast (which we call the singular polynomial), where K is a generalized Kasteleyn matrix for a planar bipartite graph. We also present a q-version of these ideas and a few results concerning tilings of special regions such as rectangles.
dc.description15 pages, 4 figures
dc.identifierhttps://arxiv.org/abs/math/0101002
dc.identifierhttp://arxiv.org/abs/math/0101002
dc.identifierJournal of Algebraic Combinatorics, 16(2): 195-207; Sep 2002
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/60666
dc.subjectCombinatorics
dc.subject05B45
dc.titleSingular polynomials of generalized Kasteleyn matrices
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