Flag enumerations of matroid base polytopes
Sangwook Kim

TL;DR
This paper investigates the combinatorial and geometric structures of matroid base polytopes, focusing on flag structures, face descriptions, hyperplane splits, and the cd-index, especially for rank 2 matroids.
Contribution
It provides new characterizations of faces and splits of matroid base polytopes and relates the cd-index to these structures, advancing understanding of their combinatorial properties.
Findings
Faces of matroid base polytopes are described in terms of matroid data.
Conditions for hyperplane splits of matroid base polytopes are established.
The cd-index of a matroid base polytope of rank 2 is explicitly expressed.
Abstract
In this paper, we study flag structures of matroid base polytopes. We describe faces of matroid base polytopes in terms of matroid data, and give conditions for hyperplane splits of matroid base polytopes. Also, we show how the cd-index of a polytope can be expressed when a polytope is split by a hyperplane, and apply these to the cd-index of a matroid base polytope of a rank 2 matroid.
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
TopicsPolynomial and algebraic computation · Computational Geometry and Mesh Generation · Advanced Combinatorial Mathematics
