Rowmotion and increasing labeling promotion
| Autor: | Kevin Dilks, Corey Vorland, Jessica Striker |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Generalization
Group (mathematics) 010102 general mathematics 0102 computer and information sciences Cartesian product 01 natural sciences Action (physics) Theoretical Computer Science Combinatorics symbols.namesake Computational Theory and Mathematics Hyperplane 010201 computation theory & mathematics Product (mathematics) FOS: Mathematics symbols Mathematics - Combinatorics Discrete Mathematics and Combinatorics Order (group theory) Combinatorics (math.CO) 0101 mathematics Partially ordered set Mathematics |
| Zdroj: | Journal of Combinatorial Theory, Series A. 164:72-108 |
| ISSN: | 0097-3165 |
| DOI: | 10.1016/j.jcta.2018.12.007 |
| Popis: | In 2012, N. Williams and the second author showed that on order ideals of ranked partially ordered sets (posets), rowmotion is conjugate to (and thus has the same orbit structure as) a different toggle group action, which in special cases is equivalent to promotion on linear extensions of posets constructed from two chains. In 2015, O. Pechenik and the first and second authors extended these results to show that increasing tableaux under K-promotion naturally corresponds to order ideals in a product of three chains under a toggle group action conjugate to rowmotion they called hyperplane promotion. In this paper, we generalize these results to the setting of arbitrary increasing labelings of any finite poset with given restrictions on the labels. We define a generalization of K-promotion in this setting and show it corresponds to a toggle group action we call toggle-promotion on order ideals of an associated poset. When the restrictions on labels are particularly nice (for example, specifying a global bound on all labels used), we show that toggle-promotion is conjugate to rowmotion. Additionally, we show that any poset that can be nicely embedded into a Cartesian product has a natural toggle-promotion action conjuate to rowmotion. 29 pages, 14 figures |
| Databáze: | OpenAIRE |
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