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Bounds for the connective constant of the hexagonal lattice
Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Mathematics and Computer Science, Department of Mathematics. Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Mathematics and Computer Science, Department of Mathematics, Mathematical Statistics. Matematisk statistik.
Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Mathematics and Computer Science, Department of Mathematics. Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Mathematics and Computer Science, Department of Mathematics, Mathematical Statistics. Matematisk statistik.
2004 (English)In: J.\ Phys. A: Math. Gen., Vol. 37, 549- p.Article in journal (Refereed) Published
Abstract [en]

We give improved bounds for the connective constant of the hexagonal lattice. The lower bound is found by using Kesten's method of irreducible bridges and by determining generating functions for bridges on one-dimensional lattices.

The upper bound is obtained as the largest eigenvalue of a certain transfer matrix. Using a relation between the hexagonal and the $(3.12^2)$ lattices, we also give bounds for the connective constant of the latter lattice.

Place, publisher, year, edition, pages
2004. Vol. 37, 549- p.
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:uu:diva-70897DOI: doi:10.1088/0305-4470/37/3/001OAI: oai:DiVA.org:uu-70897DiVA: diva2:98808
Available from: 2007-01-18 Created: 2007-01-18 Last updated: 2011-01-12

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Alm, Sven Erick

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