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A generalization of the Whitney rank generating function

Published online by Cambridge University Press:  24 October 2008

G. E. Farr
G. E. Farr
Affiliation:
CMR Group, Communications Division, ERL, Defence Science and Technology Organization, P.O. Box 4924, Kingston, A.C.T. 2604, Australia
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Abstract

The Whitney quasi-rank generating function, which generalizes the Whitney rank generating function (or Tutte polynomial) of a graph, is introduced. It is found to include as special cases the weight enumerator of a (not necessarily linear) code, the percolation probability of an arbitrary clutter and a natural generalization of the chromatic polynomial. The crucial construction, essentially equivalent to one of Kung, is a means of associating, to any function, a rank-like function with suitable properties. Some of these properties, including connections with the Hadamard transform, are discussed.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 113 , Issue 2 , March 1993 , pp. 267 - 280
Copyright
Copyright © Cambridge Philosophical Society 1993

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