TUTTE-WHITNEY POLYNOMIALS: SOME HISTORY AND GENERALIZATIONS
TUTTE-WHITNEY POLYNOMIALS: SOME HISTORY AND GENERALIZATIONS
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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