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  1. Home > Articles & Issues >
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  3. Promotion and Rowmot ...
Conference paper

Promotion and Rowmotion

Jessica Striker (1), Nathan Williams ORCID (1)
(1) School of Mathematics
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Imported on
January 31, 2017
Published on
December 31, 2011
Last modified on
March 31, 2025
Volume
DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012)
Proceedings
DOI
10.46298/dmtcs.3038
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Promotion and Rowmotion

Jessica Striker (1), Nathan Williams ORCID (1)
(1) School of Mathematics
Abstract
English
We present an equivariant bijection between two actions—promotion and rowmotion—on order ideals in certain posets. This bijection simultaneously generalizes a result of R. Stanley concerning promotion on the linear extensions of two disjoint chains and certain cases of recent work of D. Armstrong, C. Stump, and H. Thomas on noncrossing and nonnesting partitions. We apply this bijection to several classes of posets, obtaining equivariant bijections to various known objects under rotation. We extend the same idea to give an equivariant bijection between alternating sign matrices under rowmotion and under B. Wieland's gyration. Lastly, we define two actions with related orders on alternating sign matrices and totally symmetric self-complementary plane partitions.
French
Nous prèsentons une bijection èquivariante entre deux actions—promotion et rowmotion—sur les idèaux d'ordre dans certaines posets. Cette bijection gènèralise simultanèment un rèsultat de R. Stanley concernant la promotion sur les extensions linèaire de deux cha\^ınes disjointes et certains cas des travaux rècents de D. Armstrong, C. Stump, et H. Thomas sur les partitions noncroisèes et nonembo\^ıtèes. Nous appliquons cette bijection à plusieurs classes de posets pour obtenir des bijections èquivariantes a des diffèrents objets connus sous la rotation. Nous gènèralisons la même idèe pour donnè une bijection èquivariante entre les matrices à signes alternants sous rowmotion et sous la gyration de B. Wieland. Finalement, nous dèfinissons deux actions avec des ordres similaires sur les matrices à signes alternants et les partitions plane totalement symètriques et autocomplèmentaires.
Keywords
  • [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]
  • poset
  • order ideal
  • noncrossing
  • promotion
  • equivariant
  • alternating sign matrices
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