Chapter

ORBIT COUNTING AND THE TUTTE POLYNOMIAL

Peter J. Cameron

in Combinatorics, Complexity, and Chance

Published in print January 2007 | ISBN: 9780198571278
Published online September 2007 | e-ISBN: 9780191718885 | DOI: https://dx.doi.org/10.1093/acprof:oso/9780198571278.003.0001

Series: Oxford Lecture Series in Mathematics and Its Applications

 ORBIT COUNTING AND THE TUTTE POLYNOMIAL

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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

Chapter.  5128 words.  Illustrated.

Subjects: Probability and Statistics

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