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Award ID contains: 2054489

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  1. (, SIAM Journal on Discrete Mathematics)
    We define noncrossing partitions of a marked surface without punctures (interior marked points). We show that the natural partial order on noncrossing partitions is a graded lattice and describe its rank function topologically. Lower intervals in the lattice are isomorphic to products of noncrossing partition lattices of other surfaces. We similarly define noncrossing partitions of a symmetric marked surface with double points and prove some of the analogous results. The combination of symmetry and double points plays a role that one might have expected to be played by punctures. 
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    Free, publicly-accessible full text available March 31, 2026
  2. ; (, 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
  3. ; (, The Séminaire Lotharingien de Combinatoire)
    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. The model in type $$\afftype{A}$$ consists of noncrossing partitions of an annulus. In type~$$\afftype{C}$$, 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. 
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    Accepted Manuscript Full Text Available