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On a conjecture of Las Vergnas
Steven D. Noble, Gordon F. Royle
In 1988, Las Vergnas conjectured that if is a binary matroid with bicycle dimension , then for , the th derivative of the diagonal Tutte polynomial $T(M;…
An activities expansion of the transition polynomial of a multimatroid
Criel Merino, Iain Moffatt, Steven Noble
The weighted transition polynomial of a multimatroid is a generalization of the Tutte polynomial. By defining the activity of a skew class with respect to a basis in a multimatroid…
A coarse Tutte polynomial for hypermaps
Joanna A. Ellis-Monaghan, Iain Moffatt, Steven Noble
We give an analogue of the Tutte polynomial for hypermaps. This polynomial can be defined as either a sum over subhypermaps, or recursively through deletion-contraction reductions…
The complexity of the greedoid Tutte polynomial
Christopher Knapp, Steven Noble
We consider the Tutte polynomial of three classes of greedoids: those arising from rooted graphs, rooted digraphs and binary matrices. We establish the computational complexity of…
Tensor products of multimatroids and a Brylawski-type formula for the transition polynomial
Iain Moffatt, Steven Noble, Maya Thompson
Brylawski's tensor product formula expresses the Tutte polynomial of the tensor product of two graphs or matroids in terms of Tutte polynomials arising from the tensor factors. Ana…