{"pk":64909,"title":"Unimodular covers of \\(3\\)-dimensional parallelepipeds and Cayley sums","subtitle":null,"abstract":"We show that the following classes of lattice polytopes have unimodular covers, in dimension three: parallelepipeds, smooth centrally symmetric polytopes, and Cayley sums \\(\\operatorname{Cay}(P,Q)\\) where the normal fan of \\(Q\\) refines that of \\(P\\). This improves results of Beck et al. (2018) and Haase et al. (2008) where the last two classes were shown to be IDP.\n \nMathematics Subject Classifications: 52B10, 52B20, 52C17\n \nKeywords: Lattice polytopes, unimodular covers, integer decomposition property","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":"Lattice polytopes"},{"word":"unimodular covers"},{"word":"integer decomposition property"}],"section":"Research Articles","is_remote":true,"remote_url":"https://escholarship.org/uc/item/82n2n71d","frozenauthors":[{"first_name":"Giulia","middle_name":"","last_name":"Codenotti","name_suffix":"","institution":"Institute of Mathematics, Freie Universität Berlin, Germany","department":""},{"first_name":"Francisco","middle_name":"","last_name":"Santos","name_suffix":"","institution":"Department of Mathematics, Statistics and Computer Science, University of Cantabria, Spain","department":""}],"date_submitted":"2023-12-22T13:19:41Z","date_accepted":"2023-12-22T13:19:41Z","date_published":"2023-12-22T08:00:00Z","render_galley":null,"galleys":[{"label":"","type":"pdf","path":"https://journalpub.escholarship.org/combinatorial_theory/article/64909/galley/49719/download/"}]}