It is proved that the bijection presented is isomorphic to a former recursive construction on shuffles of parenthesis systems due to Cori, Dulucq and Viennot.Expand

The bijection $\Phi$ is closely related to a recent characterization of the Tutte polynomial relying on combinatorial embeddings of graphs, that is, on a choice of cyclic order of the edges around each vertex.Expand

It is proved that the Tutte polynomial equals the generating function of spanning trees counted according to embedding-activities, which is, in fact, independent of the embedding.Expand

A well-labelled positive path of size n is a pair (p,\sigma) made of a word p=p_1p_2...p_{n-1} on the alphabet {-1, 0,+1} such that the sum of the letters of any prefix is non-negative, together with… Expand

Extended abstract presented at the conference FPSAC 2016, Vancouver.
International audience
In the 1970s, Tutte developed a clever algebraic approach, based on certain " invariants " , to solve a… Expand