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

## 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 |
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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 |

Date Deposited: | 15 Oct 2010 12:01 |

URL: | http://eprints.lse.ac.uk/29561/ |

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