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- W4313443061 abstract "The noncrossing partition poset associated to a Coxeter group $W$ and Coxeter element $c$ is the interval $[1,c]_T$ in the absolute order on $W$. We construct a new model of noncrossing partititions for $W$ of classical affine type, using planar diagrams (affine types $tilde A$ and $tilde C$ in this paper and affine types $tilde D$ and $tilde B$ in the sequel). The model in type $tilde A$ consists of noncrossing partitions of an annulus. In type $tilde C$, the model consists of symmetric noncrossing partitions of an annulus or noncrossing partitions of a disk with two orbifold points. Following the lead of McCammond and Sulway, we complete $[1,c]_T$ to a lattice by factoring the translations in $[1,c]_T$, but the combinatorics of the planar diagrams leads us to make different choices about how to factor." @default.
- W4313443061 created "2023-01-06" @default.
- W4313443061 creator A5054403940 @default.
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- W4313443061 date "2022-12-28" @default.
- W4313443061 modified "2023-09-26" @default.
- W4313443061 title "Noncrossing partitions of an annulus" @default.
- W4313443061 doi "https://doi.org/10.48550/arxiv.2212.14151" @default.
- W4313443061 hasPublicationYear "2022" @default.
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