4 papers
The Active Bijection 2.b - Decomposition of activities for oriented matroids, and general definitions of the active bijection
Emeric Gioan, Michel Las Vergnas
The active bijection for oriented matroids (and real hyperplane arrangements, and graphs, as particular cases) is introduced and investigated by the authors in a series of papers.…
Computing the fully optimal spanning tree of an ordered bipolar directed graph
Emeric Gioan, Michel Las Vergnas
It has been previously shown by the authors that a directed graph on a linearly ordered set of edges (ordered graph) with adjacent unique source and sink (bipolar digraph) has a un…
The active bijection for graphs
Emeric Gioan, Michel Las Vergnas
The active bijection forms a package of results studied by the authors in a series of papers in oriented matroids. The present paper is intended to state the main results in the pa…
The Active Bijection 2.a - Decomposition of activities for matroid bases, and Tutte polynomial of a matroid in terms of beta invariants of minors
Emeric Gioan, Michel Las Vergnas
We introduce and study filtrations of a matroid on a linearly ordered ground set, which are particular sequences of nested sets. A given basis can be decomposed into a uniquely def…