A note on embracing exchange sequences in oriented matroids
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866912725971501056 |
|---|---|
| author | Bérczi, Kristóf Nádor, Benedek |
| author_facet | Bérczi, Kristóf Nádor, Benedek |
| contents | An open problem in convex geometry asks whether two simplices $A,B\subseteq\mathbb{R}^d$, both containing the origin in their convex hulls, admit a polynomial-length sequence of vertex exchanges transforming $A$ into $B$ while maintaining the origin in the convex hull throughout. We propose a matroidal generalization of the problem to oriented matroids, concerning exchange sequences between bases under sign constraints on elements appearing in certain fundamental circuits. We formulate a conjecture on the minimum length of such a sequence, and prove it for oriented graphic matroids of directed graphs. We also study connections between our conjecture and several long-standing open problems on exchange sequences between pairs of bases in unoriented matroids. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_14526 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A note on embracing exchange sequences in oriented matroids Bérczi, Kristóf Nádor, Benedek Combinatorics Discrete Mathematics An open problem in convex geometry asks whether two simplices $A,B\subseteq\mathbb{R}^d$, both containing the origin in their convex hulls, admit a polynomial-length sequence of vertex exchanges transforming $A$ into $B$ while maintaining the origin in the convex hull throughout. We propose a matroidal generalization of the problem to oriented matroids, concerning exchange sequences between bases under sign constraints on elements appearing in certain fundamental circuits. We formulate a conjecture on the minimum length of such a sequence, and prove it for oriented graphic matroids of directed graphs. We also study connections between our conjecture and several long-standing open problems on exchange sequences between pairs of bases in unoriented matroids. |
| title | A note on embracing exchange sequences in oriented matroids |
| topic | Combinatorics Discrete Mathematics |
| url | https://arxiv.org/abs/2511.14526 |