Orbit Counting and the Tutte Polynomial

Peter J. Cameron*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingChapter (peer-reviewed)peer-review

1 Citation (Scopus)


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.

Original languageEnglish
Title of host publicationCombinatorics, Complexity, and Chance
Subtitle of host publicationA Tribute to Dominic Welsh
PublisherOxford University Press
ISBN (Electronic)9780191718885
ISBN (Print)9780198571278
Publication statusPublished - 1 Sept 2007


  • Cycle index polynomial
  • Flow and tension polynomials
  • Matroid
  • Orbit counting
  • Orbital chromatic polynomial
  • Tutte polynomial


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