Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2407.01179 |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866912264196456448 |
|---|---|
| author | Abend, Lukas Schymura, Matthias |
| author_facet | Abend, Lukas Schymura, Matthias |
| contents | We are interested in algebraic properties of empty lattice simplices $Δ$, that is, $d$-dimensional lattice polytopes containing exactly $d+1$ points of the integer lattice $\mathbb{Z}^d$. The cyclicity rank of $Δ$ is the minimal number of cyclic subgroups that the quotient group of $Δ$ splits into. It is known that up to dimension $d \leq 4$, every empty lattice $d$-simplex is cyclic, meaning that its cyclicity rank is at most $1$. We determine the maximal possible cyclicity rank of an empty lattice $d$-simplex for dimensions $d \leq 8$, and determine the asymptotics of this number up to a logarithmic term. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_01179 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The cyclicity rank of empty lattice simplices Abend, Lukas Schymura, Matthias Combinatorics We are interested in algebraic properties of empty lattice simplices $Δ$, that is, $d$-dimensional lattice polytopes containing exactly $d+1$ points of the integer lattice $\mathbb{Z}^d$. The cyclicity rank of $Δ$ is the minimal number of cyclic subgroups that the quotient group of $Δ$ splits into. It is known that up to dimension $d \leq 4$, every empty lattice $d$-simplex is cyclic, meaning that its cyclicity rank is at most $1$. We determine the maximal possible cyclicity rank of an empty lattice $d$-simplex for dimensions $d \leq 8$, and determine the asymptotics of this number up to a logarithmic term. |
| title | The cyclicity rank of empty lattice simplices |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2407.01179 |