{"pk":64879,"title":"Extensions of the Kahn-Saks inequality for posets of width two","subtitle":null,"abstract":"The Kahn-Saks inequality is a classical result on the number of linear extensions of finite posets. We give a new proof of this inequality for posets of width two and both elements in the same chain using explicit injections of lattice paths. As a consequence we obtain a \\(q\\)-analogue, a multivariate generalization and an equality condition in this case. We also discuss the equality conditions of the Kahn-Saks inequality for general posets and prove several implications between conditions conjectured to be equivalent.\n \nMathematics Subject Classifications: 05A15, 05A19, 05A20, 05A30, 06A07\n \nKeywords: Poset inequality, Stanley's inequality, Kahn-Saks inequality, log-concavity, q-analogues, equality conditions, lattice paths","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":"Poset inequality"},{"word":"Stanley's inequality"},{"word":"Kahn-Saks inequality"},{"word":"log-concavity"},{"word":"q-analogues"},{"word":"equality conditions"},{"word":"lattice paths"}],"section":"Research Articles","is_remote":true,"remote_url":"https://escholarship.org/uc/item/4bd6q0m1","frozenauthors":[{"first_name":"Swee","middle_name":"Hong","last_name":"Chan","name_suffix":"","institution":"Department of Mathematics, Rutgers University, New Jersey, U.S.A.","department":""},{"first_name":"Igor","middle_name":"","last_name":"Pak","name_suffix":"","institution":"Department of Mathematics, UCLA, California, U.S.A.","department":""},{"first_name":"Greta","middle_name":"","last_name":"Panova","name_suffix":"","institution":"Department of Mathematics, University of Southern California, California, U.S.A.","department":""}],"date_submitted":"2023-03-14T15:37:03Z","date_accepted":"2023-03-14T15:37:03Z","date_published":"2023-03-15T07:00:00Z","render_galley":null,"galleys":[{"label":"","type":"pdf","path":"https://journalpub.escholarship.org/combinatorial_theory/article/64879/galley/49689/download/"}]}