On the Order of P-Strict Promotion on $V\times [\ell]$
Fuente:
arXiv
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2023
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866916256195543040 |
|---|---|
| author | Adenbaum, Ben |
| author_facet | Adenbaum, Ben |
| contents | Denote by $V$ the poset consisting of the elements $\{A,B,C\}$ with cover relations $\{A\lessdot B, A\lessdot C\}$. We show that $P$-strict promotion, as defined by Bernstein, Striker, and Vorland, on $P$-strict labelings of $V\times [\ell]$ with labels in the set $[q]$ has order $2q$ for every $\ell\ge 1$ and $q\ge 3$ as conjectured by Bernstein, Striker, and Vorland. This resolves the equivalent conjecture of Hopkins that the order of piecewise-linear rowmotion on the order polytope of $V\times [k]$ has order $2(k+2)$ for all $k\ge 1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_08757 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the Order of P-Strict Promotion on $V\times [\ell]$ Adenbaum, Ben Combinatorics 05E18, 06A07 Denote by $V$ the poset consisting of the elements $\{A,B,C\}$ with cover relations $\{A\lessdot B, A\lessdot C\}$. We show that $P$-strict promotion, as defined by Bernstein, Striker, and Vorland, on $P$-strict labelings of $V\times [\ell]$ with labels in the set $[q]$ has order $2q$ for every $\ell\ge 1$ and $q\ge 3$ as conjectured by Bernstein, Striker, and Vorland. This resolves the equivalent conjecture of Hopkins that the order of piecewise-linear rowmotion on the order polytope of $V\times [k]$ has order $2(k+2)$ for all $k\ge 1$. |
| title | On the Order of P-Strict Promotion on $V\times [\ell]$ |
| topic | Combinatorics 05E18, 06A07 |
| url | https://arxiv.org/abs/2308.08757 |