Tóthmérész, Lilla (2024) A geometric proof for the root-independence of the greedoid polynomial of Eulerian branching greedoids. JOURNAL OF COMBINATORIAL THEORY SERIES A, 206. No.-105891. ISSN 0097-3165
|
Text
1-s2.0-S009731652400030X-main1.pdf - Published Version Available under License Creative Commons Attribution Non-commercial. Download (455kB) | Preview |
Abstract
We define the root polytope of a regular oriented matroid, and show that the greedoid polynomial of an Eulerian branching greedoid rooted at vertex is equivalent to the ⁎ -polynomial of the root polytope of the dual of the graphic matroid. As the definition of the root polytope is independent of the vertex , this gives a geometric proof for the root-independence of the greedoid polynomial for Eulerian branching greedoids, a fact which was first proved by Swee Hong Chan, Kévin Perrot and Trung Van Pham using sandpile models. We also obtain that the greedoid polynomial does not change if we reverse every edge of an Eulerian digraph.
Item Type: | Article |
---|---|
Uncontrolled Keywords: | Root polytope, Triangulation, Regular matroid, Greedoid |
Subjects: | Q Science / természettudomány > QA Mathematics / matematika |
SWORD Depositor: | MTMT SWORD |
Depositing User: | MTMT SWORD |
Date Deposited: | 30 Sep 2024 06:46 |
Last Modified: | 30 Sep 2024 06:46 |
URI: | https://real.mtak.hu/id/eprint/206434 |
Actions (login required)
![]() |
Edit Item |