On the order of \(P\)-strict promotion on \(\mathsf{V}\times [\ell]\)
The electronic journal of combinatorics, Tome 32 (2025) no. 2
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 a consequence of results of Bernstein, Striker, and Vorland, this result proves that piecewise-linear rowmotion on $V\times [k]$ has order $2(k+2)$ for all $k\ge 1$, as conjectured by Hopkins.
DOI :
10.37236/13044
Classification :
05E18, 06A07
Mots-clés : rowmotion, Hopkins conjecture
Mots-clés : rowmotion, Hopkins conjecture
Affiliations des auteurs :
Benjamin Adenbaum 1
@article{10_37236_13044,
author = {Benjamin Adenbaum},
title = {On the order of {\(P\)-strict} promotion on {\(\mathsf{V}\times} [\ell]\)},
journal = {The electronic journal of combinatorics},
year = {2025},
volume = {32},
number = {2},
doi = {10.37236/13044},
zbl = {1564.05368},
url = {http://geodesic.mathdoc.fr/articles/10.37236/13044/}
}
Benjamin Adenbaum. On the order of \(P\)-strict promotion on \(\mathsf{V}\times [\ell]\). The electronic journal of combinatorics, Tome 32 (2025) no. 2. doi: 10.37236/13044
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