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Combinatorics, Complexity, and ChanceA Tribute to Dominic Welsh$
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Geoffrey Grimmett and Colin McDiarmid

Print publication date: 2007

Print ISBN-13: 9780198571278

Published to Oxford Scholarship Online: September 2007

DOI: 10.1093/acprof:oso/9780198571278.001.0001

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ORBIT COUNTING AND THE TUTTE POLYNOMIAL

ORBIT COUNTING AND THE TUTTE POLYNOMIAL

Chapter:
(p.1) 1 ORBIT COUNTING AND THE TUTTE POLYNOMIAL
Source:
Combinatorics, Complexity, and Chance
Author(s):

Peter J. Cameron

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198571278.003.0001

This chapter summarizes the various attempts to extend the Tutte polynomial of a matroid to a polynomial which counts orbits of a group on various sets of objects that the usual Tutte polynomial counts. In other words, the aim is to produce a hybrid of the Tutte polynomial and the cycle index polynomial. There have been various attempts at this, some of which are good for some aims but not for others.

Keywords:   Tutte polynomial, matroid, orbit counting, cycle index polynomial, orbital chromatic polynomial, flow and tension polynomials

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