$P$-strict promotion and $Q$-partition rowmotion: the graded case
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2022
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| _version_ | 1866914825665249280 |
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| author | Bernstein, Joseph Striker, Jessica Vorland, Corey |
| author_facet | Bernstein, Joseph Striker, Jessica Vorland, Corey |
| contents | Promotion and rowmotion are intriguing actions in dynamical algebraic combinatorics which have inspired much work in recent years. In this paper, we study $P$-strict labelings of a finite, graded poset $P$ of rank $n$ and labels at most $q$, which generalize semistandard Young tableaux with $n$ rows and entries at most $q$, under promotion. These $P$-strict labelings are in equivariant bijection with $Q$-partitions under rowmotion, where $Q$ equals the product of $P$ and a chain of $q-n-1$ elements. We study the case where $P$ equals the product of chains in detail, yielding new homomesy and order results in the realm of tableaux and beyond. Furthermore, we apply the bijection to the cases in which $P$ is a minuscule poset and when $P$ is the three element $V$ poset. Finally, we give resonance results for promotion on $P$-strict labelings and rowmotion on $Q$-partitions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2205_04938 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | $P$-strict promotion and $Q$-partition rowmotion: the graded case Bernstein, Joseph Striker, Jessica Vorland, Corey Combinatorics 05E18 Promotion and rowmotion are intriguing actions in dynamical algebraic combinatorics which have inspired much work in recent years. In this paper, we study $P$-strict labelings of a finite, graded poset $P$ of rank $n$ and labels at most $q$, which generalize semistandard Young tableaux with $n$ rows and entries at most $q$, under promotion. These $P$-strict labelings are in equivariant bijection with $Q$-partitions under rowmotion, where $Q$ equals the product of $P$ and a chain of $q-n-1$ elements. We study the case where $P$ equals the product of chains in detail, yielding new homomesy and order results in the realm of tableaux and beyond. Furthermore, we apply the bijection to the cases in which $P$ is a minuscule poset and when $P$ is the three element $V$ poset. Finally, we give resonance results for promotion on $P$-strict labelings and rowmotion on $Q$-partitions. |
| title | $P$-strict promotion and $Q$-partition rowmotion: the graded case |
| topic | Combinatorics 05E18 |
| url | https://arxiv.org/abs/2205.04938 |