Tutte polynomials of bracelets
Norman Biggs
DOI: 10.1007/s10801-010-0220-1
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 π of a nonnegative integer \ell \leq b:
| ( x -1) T( G n; x, y)= å p m p( x, y)\operatorname tr( N p( x, y)) n. (x-1)T(G_n;x,y)=\sum_{π}m_{π}(x,y)\operatorname {tr}\bigl(N_{π}(x,y)\bigr)^n.
Pages: 389–398 Keywords: keywords tutte polynomial; Potts model; transfer matrix; Specht modules Full Text: PDF References1. Biggs, N.L.: Interaction Models. University Press, Cambridge (1977)
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