Modifications of Tutte–Grothendieck invariants and Tutte polynomials

Abstract

Generalized Tutte–Grothendieck invariants are mappings from the class of matroids to a commutative ring that are characterized recursively by contraction–deletion rules. Well known examples are Tutte, chromatic, tension and flow polynomials. In general, the rule consists of three formulas valid separately for loops, isthmuses, and the ordinary elements. We show that each generalized Tutte–Grothendieck invariant thus also Tutte polynomials on matroids can be transformed so that the contraction–deletion rule for loops (isthmuses) coincides with the general case.