Séminaire Lotharingien de Combinatoire, 89B.18 (2023), 12 pp.
Laura G. Brestensky and Nathan Reading
Noncrossing Partitions of an Annulus
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 partitions for W of classical affine type, using planar diagrams.
The model in type A~ consists of noncrossing partitions of an annulus.
In type 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.
Received: November 15, 2022.
Accepted: February 20, 2023.
Final version: April 1, 2023.
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