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An application of renewal sequences to the dimer problem

Contributed Papers

Part of the Lecture Notes in Mathematics book series (LNM,volume 748)

Abstract

The theory of renewal sequences is used to obtain some exact results for the number of dimer and monomer-dimer configurations on blocks and rods in the hypercubical lattice and these results, in turn, are applied to give lower bounds for the dimer problem on the unrestricted lattice.

Keywords

  • Transfer Matrix Method
  • Hypercubical Lattice
  • Critical Configuration
  • Dime Configuration
  • Renewal Sequence

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© 1979 Springer-Verlag

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Rogers, D.G. (1979). An application of renewal sequences to the dimer problem. In: Horadam, A.F., Wallis, W.D. (eds) Combinatorial Mathematics VI. Lecture Notes in Mathematics, vol 748. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0102693

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  • DOI: https://doi.org/10.1007/BFb0102693

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-09555-2

  • Online ISBN: 978-3-540-34857-3

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