{"pk":64972,"title":"Noncrossing partitions of an annulus","subtitle":null,"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 \\(\\widetilde{A}\\) and \\(\\widetilde{C}\\) in this paper and affine types \\(\\widetilde{D}\\) and \\(\\widetilde{B}\\) in the sequel). The model in type \\(\\widetilde{A}\\) consists of noncrossing partitions of an annulus. In type \\(\\widetilde{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.\n \nMathematics Subject Classifications: 20F55, 05E16, 20F36\n \nKeywords: Absolute order, affine Coxeter group, annulus, noncrossing partition","language":"en","license":{"name":"Creative Commons Attribution 4.0","short_name":"CC BY 4.0","text":"Attribution — You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.\n\nNo additional restrictions — You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.","url":"https://creativecommons.org/licenses/by/4.0"},"keywords":[{"word":"Absolute order"},{"word":"affine Coxeter group"},{"word":"annulus"},{"word":"noncrossing partition"}],"section":"Research Articles","is_remote":true,"remote_url":"https://escholarship.org/uc/item/06h8q34n","frozenauthors":[{"first_name":"Laura","middle_name":"G.","last_name":"Brestensky","name_suffix":"","institution":"Department of Mathematics, North Carolina State University, Raleigh, North Carolina, U.S.A.","department":""},{"first_name":"Nathan","middle_name":"","last_name":"Reading","name_suffix":"","institution":"Department of Mathematics, North Carolina State University, Raleigh, North Carolina, U.S.A.","department":""}],"date_submitted":"2025-03-14T21:49:16+05:00","date_accepted":"2025-03-14T21:49:16+05:00","date_published":"2025-03-15T12:00:00+05:00","render_galley":null,"galleys":[{"label":"","type":"pdf","path":"https://journalpub.escholarship.org/combinatorial_theory/article/64972/galley/49782/download/"}]}