{"pk":64863,"title":"The polyhedral tree complex","subtitle":null,"abstract":"The tree complex is a simplicial complex defined in recent work of Belk, Lanier, Margalit, and Winarski with applications to mapping class groups and complex dynamics. This article introduces a connection between this setting and the convex polytopes known as associahedra and cyclohedra. Specifically, we describe a characterization of these polytopes using planar embeddings of trees and show that the tree complex is the barycentric subdivision of a polyhedral cell complex for which the cells are products of associahedra and cyclohedra.\n \nMathematics Subject Classifications: 05C05, 05C10, 20F65, 52B11\n \nKeywords: Associahedra, cyclohedra, planar trees, mapping class groups","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":"Associahedra"},{"word":"cyclohedra"},{"word":"planar trees"},{"word":"mapping class groups"}],"section":"Research Articles","is_remote":true,"remote_url":"https://escholarship.org/uc/item/3mx155d7","frozenauthors":[{"first_name":"Michael","middle_name":"","last_name":"Dougherty","name_suffix":"","institution":"Department of Mathematics, Lafayette College, Easton, PA, U.S.A.","department":""}],"date_submitted":"2022-10-11T16:08:32Z","date_accepted":"2022-10-11T16:08:32Z","date_published":"2022-10-15T07:00:00Z","render_galley":null,"galleys":[{"label":"","type":"pdf","path":"https://journalpub.escholarship.org/combinatorial_theory/article/64863/galley/49673/download/"}]}