Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2018
|
| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/1806.05239 |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866929459342344192 |
|---|---|
| author | Johnson, Wayne A. Mogilski, Wiktor J. |
| author_facet | Johnson, Wayne A. Mogilski, Wiktor J. |
| contents | We study the exponential Hilbert series (both coarsely- and finely-graded) of the Stanley-Reisner ring of an abstract simplicial complex, $Δ$, and we introduce the $e$-vector of $Δ$, which relates to the coefficients of the exponential Hilbert series. We explore the relationship of the $e$-vector with the classical $f$-vector and $h$-vector of $Δ$ while simultaneously investigating the geometric information that the $e$-vector encodes about $Δ$. We then prove a simple combinatorial identity for the $e$-vector in the case where $Δ$ is an Eulerian manifold. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1806_05239 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | The $e$-vector of a simplicial complex Johnson, Wayne A. Mogilski, Wiktor J. Combinatorics 05E45 We study the exponential Hilbert series (both coarsely- and finely-graded) of the Stanley-Reisner ring of an abstract simplicial complex, $Δ$, and we introduce the $e$-vector of $Δ$, which relates to the coefficients of the exponential Hilbert series. We explore the relationship of the $e$-vector with the classical $f$-vector and $h$-vector of $Δ$ while simultaneously investigating the geometric information that the $e$-vector encodes about $Δ$. We then prove a simple combinatorial identity for the $e$-vector in the case where $Δ$ is an Eulerian manifold. |
| title | The $e$-vector of a simplicial complex |
| topic | Combinatorics 05E45 |
| url | https://arxiv.org/abs/1806.05239 |