Alex Fink

Tutte characters for 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.