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Journal of Algebraic Combinatorics

, Volume 16, Issue 2, pp 195–207 | Cite as

Singular Polynomials of Generalized Kasteleyn Matrices

  • Nicolau C. Saldanha
Article

Abstract

Kasteleyn 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* (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.

domino tilings dimers Kasteleyn matrix singular values 

References

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Copyright information

© Kluwer Academic Publishers 2002

Authors and Affiliations

  • Nicolau C. Saldanha
    • 1
  1. 1.Depto. de MatemáticaRio de Janeiro RJBrazil

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