{"pk":64888,"title":"An exact characterization of saturation for permutation matrices","subtitle":null,"abstract":"A 0-1 matrix \\(M\\) contains a 0-1 matrix pattern \\(P\\) if we can obtain \\(P\\) from \\(M\\) by deleting rows and/or columns and turning arbitrary 1-entries into 0s. The saturation function \\(\\mathrm{sat}(P,n)\\) for a 0-1 matrix pattern \\(P\\) indicates the minimum number of 1s in an \\(n \\times n\\) 0-1 matrix that does not contain \\(P\\), but changing any 0-entry into a 1-entry creates an occurrence of \\(P\\). Fulek and Keszegh recently showed that each pattern has a saturation function either in \\(\\mathcal{O}(1)\\) or in \\(\\Theta(n)\\). We fully classify the saturation functions of permutation matrices.\n \nMathematics Subject Classifications: 05D99\n \nKeywords: Forbidden submatrices, saturation","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":"Forbidden submatrices"},{"word":"saturation"}],"section":"Research Articles","is_remote":true,"remote_url":"https://escholarship.org/uc/item/1dd7c0q9","frozenauthors":[{"first_name":"Benjamin","middle_name":"Aram","last_name":"Berendsohn","name_suffix":"","institution":"Freie Universität Berlin, Institut für Informatik, Berlin, Germany","department":""}],"date_submitted":"2023-03-14T16:48:17Z","date_accepted":"2023-03-14T16:48:17Z","date_published":"2023-03-15T07:00:00Z","render_galley":null,"galleys":[{"label":"","type":"pdf","path":"https://journalpub.escholarship.org/combinatorial_theory/article/64888/galley/49698/download/"}]}