On a matching arrangement of a graph and LP-orientations of a matching polyhedron
Aleksey Bolotnikov
TL;DR
This paper establishes a bijection between regions of the matching arrangement and LP-orientations of the matching polyhedron, enabling calculation of LP-orientation counts via the characteristic polynomial of the arrangement.
Contribution
It introduces a novel bijection linking matching arrangements and LP-orientations of the matching polyhedron, facilitating enumeration of orientations.
Findings
Bijection between matching arrangement regions and LP-orientations
Calculation of LP-orientation counts using characteristic polynomial
Enhanced understanding of the structure of matching polyhedra
Abstract
This paper contains a description of a connection between the matching arrangement and the matching polyhedron. A bijection between regions of the matching arragement and LP-orientations of the matching polyhedron is constructed. This bijection allows to calculate the number of LP-orientations of the matching polyhedron with the characteristic polynomial of the matching arrangement.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsComputational Geometry and Mesh Generation · Advanced Theoretical and Applied Studies in Material Sciences and Geometry · Optimization and Packing Problems