Interlace Polynomials for Delta-Matroids

Details Interlace Polynomials for Delta-Matroids Interlace Polynomials for Delta-Matroids

2010-10-22

arxiv.org/abs/1010.4678v3

Mathematics

Combinatorics

Changes w.r.t. v2: consequences of vf-closedness of binary matroids are discussed, and moreover some smaller changes are made,

Scientific paper

We show that the (single variable) interlace polynomial and several related graph polynomials may be defined for set systems (or more specifically, delta-matroids) in general. In this way, and using combinatorial properties of set systems and delta-matroids rather than graph theoretical arguments, we find that various known results about these polynomials, including their recursive relations, are both more efficiently and more generally obtained. In addition, we obtain several interrelationships and results for polynomials on set systems (and delta-matroids) that correspond to new interrelationships and results for the corresponding polynomials on graphs. Finally, we show that the Tutte polynomial for matroids on the diagonal is a special case of the generalized interlace polynomial for delta-matroids, and we obtain in this way novel evaluations of the Tutte polynomial. In particular we prove a conjecture by Las Vergnas.

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