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- W4300650337 abstract "We study the size of certain acyclic domains that arise from geometric and combinatorial constructions. These acyclic domains consist of all permutations visited by commuting equivalence classes of maximal reduced decompositions if we consider the symmetric group and, more generally, of all c-singletons of a Cambrian lattice associated to the weak order of a finite Coxeter group. For this reason, we call these sets Cambrian acyclic domains. Extending a closed formula of Galambos--Reiner for a particular acyclic domain called Fishburn's alternating scheme, we provide explicit formulae for the size of any Cambrian acyclic domain and characterize the Cambrian acyclic domains of minimum or maximum size." @default.
- W4300650337 created "2022-10-03" @default.
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- W4300650337 date "2018-02-22" @default.
- W4300650337 modified "2023-09-25" @default.
- W4300650337 title "Cambrian acyclic domains: counting $c$-singletons" @default.
- W4300650337 doi "https://doi.org/10.48550/arxiv.1802.07978" @default.
- W4300650337 hasPublicationYear "2018" @default.
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