Interpreting the Ehrhart coefficients of cross-polytopes
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866912755689193472 |
|---|---|
| author | Menon, Krishna Verkama, Emil |
| author_facet | Menon, Krishna Verkama, Emil |
| contents | It is known that the Ehrhart polynomials of cross-polytopes, as well as of pyramids over them, have positive coefficients. We give a combinatorial proof of this fact by showing that a scaled version of the Ehrhart polynomials are generating functions for certain colored permutations. This answers a question posed by Stanley. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_08669 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Interpreting the Ehrhart coefficients of cross-polytopes Menon, Krishna Verkama, Emil Combinatorics 05A05, 05A15, 52B05 It is known that the Ehrhart polynomials of cross-polytopes, as well as of pyramids over them, have positive coefficients. We give a combinatorial proof of this fact by showing that a scaled version of the Ehrhart polynomials are generating functions for certain colored permutations. This answers a question posed by Stanley. |
| title | Interpreting the Ehrhart coefficients of cross-polytopes |
| topic | Combinatorics 05A05, 05A15, 52B05 |
| url | https://arxiv.org/abs/2512.08669 |