| Autor: |
David Einstein, James Propp |
| Jazyk: |
angličtina |
| Rok vydání: |
2014 |
| Předmět: |
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| Zdroj: |
Discrete Mathematics & Theoretical Computer Science, Vol DMTCS Proceedings vol. AT,..., Iss Proceedings (2014) |
| Druh dokumentu: |
article |
| ISSN: |
1365-8050 |
| DOI: |
10.46298/dmtcs.2419 |
| Popis: |
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. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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