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) - LIRMM - Laboratoire d’Informatique, de Robotique et de Microélectronique de Montpellier
Preprints, Working Papers, ... Year : 2023

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

Abstract

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 and certain reorientations of M induced by the extension-lifting. This note is intended to somehow clarify and precise the geometric setting for this paper in terms of oriented matroid arrangements and oriented matroid programming, to describe and prove the main bijective result in a short simple way, and to show how it consists of combining two direct bijections and a central bijection, which is the same as a special case -practically uniform -of the bounded case of the active bijection [5, 6]. (The relation with the active bijection is addressed in [1] in an indirect and more complicated way.)
Fichier principal
Vignette du fichier
2312.07522v1.pdf (374.63 Ko) Télécharger le fichier
Origin Files produced by the author(s)
Licence

Dates and versions

lirmm-04804619 , version 1 (26-11-2024)

Licence

Identifiers

Cite

Emeric Gioan. 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). 2024. ⟨lirmm-04804619⟩
0 View
0 Download

Altmetric

Share

More