{"pk":64865,"title":"Triangulations, Order Polytopes, and Generalized Snake Posets","subtitle":null,"abstract":"This work regards the order polytopes arising from the class of generalized snake posets and their posets of meet-irreducible elements. Among generalized snake posets of the same rank, we characterize those whose order polytopes have minimal and maximal volume. We give a combinatorial characterization of the circuits in related order polytopes and then conclude that all of their triangulations are unimodular. For a generalized snake word, we count the number of flips for the canonical triangulation of these order polytopes. We determine that the flip graph of the order polytope of the poset whose lattice of upper order ideals comes from a ladder is the Cayley graph of a symmetric group. Lastly, we introduce an operation on triangulations called twists and prove that twists preserve regular triangulations.\n \nMathematics Subject Classifications: 52B20, 52B05, 52B12, 06A07\n \nKeywords: Order polytopes, triangulations, flow polytopes, circuits","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":"Order polytopes"},{"word":"triangulations"},{"word":"flow polytopes"},{"word":"circuits"}],"section":"Research Articles","is_remote":true,"remote_url":"https://escholarship.org/uc/item/9rf590vk","frozenauthors":[{"first_name":"Matias","middle_name":"","last_name":"von Bell","name_suffix":"","institution":"Institute of Geometry, Graz University of Technology, Austria","department":""},{"first_name":"Benjamin","middle_name":"","last_name":"Braun","name_suffix":"","institution":"Department of Mathematics, University of Kentucky, U.S.A.","department":""},{"first_name":"Derek","middle_name":"","last_name":"Hanely","name_suffix":"","institution":"Department of Mathematics, Penn State Behrend, U.S.A.","department":""},{"first_name":"Khrystyna","middle_name":"","last_name":"Serhiyenko","name_suffix":"","institution":"Department of Mathematics, University of Kentucky, U.S.A.","department":""},{"first_name":"Julianne","middle_name":"","last_name":"Vega","name_suffix":"","institution":"Maret School, Whasington D.C., U.S.A.","department":""},{"first_name":"Andrés","middle_name":"R.","last_name":"Vindas-Meléndez","name_suffix":"","institution":"Department of Mathematics, University of California, Berkeley, U.S.A.","department":""},{"first_name":"Martha","middle_name":"","last_name":"Yip","name_suffix":"","institution":"Department of Mathematics, University of Kentucky, U.S.A.","department":""}],"date_submitted":"2022-10-12T14:11:06Z","date_accepted":"2022-10-12T14:11:06Z","date_published":"2022-10-15T07:00:00Z","render_galley":null,"galleys":[{"label":"","type":"pdf","path":"https://journalpub.escholarship.org/combinatorial_theory/article/64865/galley/49675/download/"}]}