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Creators/Authors contains: "Brestensky, Laura G"

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  1. ; (, Combinatorial Theory)
    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 A tilde and C tilde in this paper and affine types D tilde and B tilde in the sequel). The model in type A tilde consists of noncrossing partitions of an annulus. In type C tilde, 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. 
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    Free, publicly-accessible full text available March 14, 2026