Universal Tutte characters via combinatorial coalgebras

The Tutte polynomial is a favourite invariant of matroids and graphs. So when one is working in a generalisation of these settings, for example arithmetic matroids or ribbon graphs, it is a tempting question to find a counterpart of the Tutte polynomial; answers have been given in many cases. Our work unifies these answers, providing general machinery to turn a combinatorial object with "minor" operations into a coalgebra, and from that coalgebra extract the most general possible Tutte-like invariant. We build on earlier work by Krajewski, Moffatt, and Tanasa, who used Hopf algebras for this purpose.

Joint with Clément Dupont and Luca Moci.