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Tutte polynomials of bracelets

Biggs, Norman (2010) Tutte polynomials of bracelets. Journal of Algebraic Combinatorics, 32 (3). pp. 389-398. ISSN 0925-9899

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Abstract

The identity linking the Tutte polynomial with the Potts model on a graph implies the existence of a decomposition resembling that previously obtained for the chromatic polynomial. Specifically, let {G (n) } be a family of bracelets in which the base graph has b vertices. It is shown here (Theorems 3 and 4) that the Tutte polynomial of G (n) can be written as a sum of terms, one for each partition pi of a nonnegative integer a""a parts per thousand currency signb: The matrices N (pi) (x,y) are (essentially) the constituents of a 'Potts transfer matrix', and a formula for their sizes is obtained. The multiplicities m (pi) (x,y) are obtained by substituting k=(x-1)(y-1) in the expressions m (pi) (k) previously obtained in the chromatic case. As an illustration, explicit calculations are given for some small bracelets.

Item Type: Article
Official URL: http://www.springerlink.com/content/100277/
Additional Information: © 2010 Springer Science+Business Media, LLC
Library of Congress subject classification: Q Science > QA Mathematics
Sets: Departments > Mathematics
Rights: http://www.lse.ac.uk/library/usingTheLibrary/academicSupport/OA/depositYourResearch.aspx
Identification Number: UT ISI:000281859000005
Date Deposited: 15 Oct 2010 12:01
URL: http://eprints.lse.ac.uk/29561/

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