David Einstein ; James Propp - Piecewise-linear and birational toggling

dmtcs:2419 - Discrete Mathematics & Theoretical Computer Science, January 1, 2014, DMTCS Proceedings vol. AT, 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014) - https://doi.org/10.46298/dmtcs.2419
Piecewise-linear and birational togglingArticle

Authors: David Einstein 1; James Propp 1

  • 1 Department of Mathematics [Lowell]

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.


Volume: DMTCS Proceedings vol. AT, 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014)
Section: Proceedings
Published on: January 1, 2014
Imported on: November 21, 2016
Keywords: tropicalization,promotion,rowmotion,order polytope,order ideal,poset,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM],[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO]

5 Documents citing this article

Consultation statistics

This page has been seen 229 times.
This article's PDF has been downloaded 411 times.