7 citations · 19 across the 12 of their papers we have counts for
13 papers
Short rewriting, and geometric explanations related to the active bijection, for: Extension-lifting bijections for oriented matroids, by S. Backman, F. Santos, C.H. Yuen, arXiv:1904.03562v2 (October 29, 2023)
Emeric Gioan
For an oriented matroid M, and given a generic single element extension and a generic single element lifting of M, the main result of [1] provides a bijection between bases of M an…
Rectangles, integer vectors and hyperplanes of the hypercube
E. Gioan, I. P. Silva
We introduce a family of nonnegative integer vectors - primitive vectors - defining hyperplanes of the real affine cube over and study their properties with respe…
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.…
On Tutte polynomial expansion formulas in perspectives of matroids and oriented matroids
Emeric Gioan
We introduce the active partition of the ground set of an oriented matroid perspective (or quotient, or strong map) on a linearly ordered ground set. The reorientations obtained by…
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…