Orbit Counting and the Tutte Polynomial

Peter J. Cameron

doi:10.1093/acprof:oso/9780198571278.003.0001

Orbit Counting and the Tutte Polynomial

Peter J. Cameron^*

^*Corresponding author for this work

Centre for Interdisciplinary Research in Computational Algebra

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

Abstract

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 language	English
Title of host publication	Combinatorics, Complexity, and Chance
Subtitle of host publication	A Tribute to Dominic Welsh
Publisher	Oxford University Press
ISBN (Electronic)	9780191718885
ISBN (Print)	9780198571278
DOIs	https://doi.org/10.1093/acprof:oso/9780198571278.003.0001
Publication status	Published - 1 Sept 2007

Keywords

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

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10.1093/acprof:oso/9780198571278.003.0001

Cite this

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abstract = "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.",

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AB - 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.

KW - Cycle index polynomial

KW - Flow and tension polynomials

KW - Matroid

KW - Orbit counting

KW - Orbital chromatic polynomial

KW - Tutte polynomial

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BT - Combinatorics, Complexity, and Chance

PB - Oxford University Press

ER -

Orbit Counting and the Tutte Polynomial

Abstract

Keywords

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