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• W2463036700 abstract "We survey recent work within the area of algebraic combinatorics that has the flavor of discrete dynamical systems, with a particular focus on the homomesy phenomenon codified in 2013 by James Propp and the author. In these situations, a group action on a set of combinatorial objects partitions them into orbits, and we search for statistics that are homomesic, i.e., have the same average value over each orbit. We give a number of examples, many very explicit, to illustrate the wide range of the phenomenon and its connections to other parts of combinatorics. In particular, we look at several actions that can be defined as a product of toggles, involutions on the set that make only local changes. This allows us to lift the well-known poset maps of rowmotion and promotion to the piecewise-linear and birational settings, where periodicity becomes much harder to prove, and homomesy continues to hold. Some of the examples have strong connections with the representation theory of semisimple Lie algebras, and others to cluster algebras via Y -systems." @default.
• W2463036700 created "2016-07-22" @default.
• W2463036700 creator A5071443532 @default.
• W2463036700 date "2016-01-01" @default.
• W2463036700 modified "2023-09-30" @default.
• W2463036700 title "Dynamical algebraic combinatorics and the homomesy phenomenon" @default.
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• W2463036700 doi "https://doi.org/10.1007/978-3-319-24298-9_25" @default.
• W2463036700 hasPublicationYear "2016" @default.
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