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Promotion and rowmotion - an ocean of notions

Banff International Research Station for Mathematical Innovation and Discovery

In this talk, we introduce Dynamical Algebraic Combinatorics by investigating ever more general domains in which the actions of promotion on tableaux (or tableaux-like objects) and rowmotion on order ideals (or generalizations of order ideals) correspond. These domains include: (1) promotion on $2\times n$ standard Young tableaux and rowmotion on order ideals of the Type A root poset, (2) K-promotion on rectangular increasing tableaux and rowmotion on order ideals of the product of three chains poset, (3) generalized promotion on increasing labelings of a finite poset and rowmotion on order ideals of a corresponding poset, and, finally, (4) promotion on new objects we call P-strict labelings (named in analogy to column-strict tableaux) and piecewise-linear rowmotion on P-partitions of a corresponding poset. This talk will be accessible to those with little DAC background and of interest to those working in the field. It includes joint works with J. Bernstein, K. Dilks, O. Pechenik, C. Vorland, and N. Williams.

Mathematics; Combinatorics; Dynamical systems and ergodic theory

video/mp4

Author affiliation: North Dakota State University

2021-04-18

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/77821

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/