Monte Carlo estimation of the number of tatami tilings

Kenji Kimura () and Saburo Higuchi ()
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Kenji Kimura: Department of Applied Mathematics and Informatics, Ryukoku University, Otsu, Shiga 520-2194, Japan
Saburo Higuchi: Department of Applied Mathematics and Informatics, Ryukoku University, Otsu, Shiga 520-2194, Japan

International Journal of Modern Physics C (IJMPC), 2016, vol. 27, issue 11, 1-14

Abstract: Motivated by the way Japanese tatami mats are placed on the floor, we consider domino tilings with a constraint and estimate the number of such tilings of plane regions. We map the system onto a monomer-dimer model with a novel local interaction on the dual lattice. We make use of a variant of the Hamiltonian replica exchange Monte Carlo method where data for ferromagnetic and anti-ferromagnetic models are combined to make a single family of histograms. The properties of the density of states is studied beyond exact enumeration and combinatorial methods. The logarithm of the number of the tilings is linear in the boundary length of the region for all the regions studied.

Keywords: Monte Carlo; monomer–dimer tiling; tatami tiling (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1142/S012918311650128X

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