![]() |
Discrete Mathematics & Theoretical Computer Science |
We define piecewise-linear and birational analogues of toggle-involutions, rowmotion, and promotion on order ideals of a poset $P$ as studied by Striker and Williams. Piecewise-linear rowmotion relates to Stanley's transfer map for order polytopes; piecewise-linear promotion relates to Schützenberger promotion for semistandard Young tableaux. When $P = [a] \times [b]$, a reciprocal symmetry property recently proved by Grinberg and Roby implies that birational rowmotion (and consequently piecewise-linear rowmotion) is of order $a+b$. We prove some homomesy results, showing that for certain functions $f$, the average of $f$ over each rowmotion/promotion orbit is independent of the orbit chosen.
Source : ScholeXplorer
IsRelatedTo ARXIV 2002.04810 Source : ScholeXplorer IsRelatedTo DOI 10.37236/9769 Source : ScholeXplorer IsRelatedTo DOI 10.48550/arxiv.2002.04810
|