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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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TUTTE-WHITNEY POLYNOMIALS: SOME HISTORY AND GENERALIZATIONS

TUTTE-WHITNEY POLYNOMIALS: SOME HISTORY AND GENERALIZATIONS

Chapter:
(p.28) 3 TUTTE-WHITNEY POLYNOMIALS: SOME HISTORY AND GENERALIZATIONS
Source:
Combinatorics, Complexity, and Chance
Author(s):

Graham E. Farr

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198571278.003.0003

The Tutte-Whitney polynomials play a key role in the study of counting problems on graphs, and have close connections with statistical mechanics and knot theory. This chapter briefly reviews their history and outlines a number of generalizations. It then describes some generalized Tutte-Whitney functions and extends some of these further. These functions are defined for arbitrary collections of sets and for arbitrary binary functions, and have some of the characteristic elements of Tutte-Whitney theory, including interesting partial evaluations and deletion-contraction relations.

Keywords:   Tutte-Whitney polynomials, counting, sets, binary functions, univariate polynomials, binary matroids

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