Rowmotion in slow motion
arXiv:1712.10123 · doi:10.1112/plms.12251
Abstract
Rowmotion is a simple cyclic action on the distributive lattice of order ideals of a poset: it sends the order ideal x to the order ideal generated by the minimal elements not in x. It can also be computed in "slow motion" as a sequence of local moves. We use the setting of trim lattices to generalize both definitions of rowmotion, proving many structural results along the way. We introduce a flag simplicial complex (similar to the canonical join complex of a semidistributive lattice), and relate our results to recent work of Barnard by proving that extremal semidistributive lattices are trim. As a corollary, we prove that if A is a representation finite algebra and mod A has no cycles, then the torsion classes of A ordered by inclusion form a trim lattice.
arXiv comment29 pages, 8 figures; some typos fixed
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Cited by in corpus (12)
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- The CDE property for skew vexillary permutations
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- The birational Lalanne-Kreweras involution
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- The fundamental theorem of finite semidistributive lattices
- Ungarian Markov Chains
- Extremality, Left-Modularity and Semidistributivity
- Bubble Lattices I: Structure
- Rowmotion Markov Chains