Computing the Tutte polynomial of Archimedean tilings

We describe an algorithm to compute the Tutte polynomial of large fragments of Archimedean tilings by squares, triangles, hexagons and combinations thereof. Our algorithm improves a well known method for computing the Tutte polynomial of square lattices. We also address the problem of obtaining Tutt...

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Bibliographic Details
Published inApplied mathematics and computation Vol. 242; pp. 842 - 855
Main Authors Garijo, D., Gegúndez, M.E., Márquez, A., Revuelta, M.P., Sagols, F.
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.09.2014
Subjects
Archimedean tilings
Tutte polynomial
Tutte polynomial evaluations
Tutte polynomial
Tutte polynomial evaluations
Archimedean tilings
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Summary:We describe an algorithm to compute the Tutte polynomial of large fragments of Archimedean tilings by squares, triangles, hexagons and combinations thereof. Our algorithm improves a well known method for computing the Tutte polynomial of square lattices. We also address the problem of obtaining Tutte polynomial evaluations from the symbolic expressions generated by our algorithm, improving the best known lower bound for the asymptotics of the number of spanning forests, and the lower and upper bounds for the asymptotics of the number of acyclic orientations of the square lattice.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2014.06.067