{"pk":65040,"title":"Colored multiset Eulerian polynomials","subtitle":null,"abstract":"Colored multiset Eulerian polynomials are a common generalization of MacMahon's multiset Eulerian polynomials and the colored Eulerian polynomials, both of which are known to satisfy well-studied distributional properties including real-rootedness, log-concavity and unimodality. The symmetric colored multiset Eulerian polynomials are characterized and used to prove sufficient conditions for a colored multiset Eulerian polynomial to be self-interlacing. The latter property implies the aforementioned distributional properties as well as others, including the alternatingly increasing property and bi-\\(\\gamma\\)-positivity. To derive these results, multivariate generalizations of an identity due to MacMahon are deduced. The results are applied to a pair of questions, both previously studied in several special cases, that are seen to admit more general answers when framed in the context of colored multiset Eulerian polynomials. The first question pertains to \\(s\\)-Eulerian polynomials, and the second to interpretations of \\(\\gamma\\)-coefficients.\n \nMathematics Subject Classifications: 05A05, 05A15, 05A19, 52B20, 52C07\n \nKeywords: Colored permutation,    multiset permutation,   Eulerian polynomial,   real-rooted polynomial,   alternatingly increasing,   self-interlacing,   gamma positivity,   Ehrhart theory","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":"Colored permutation"},{"word":"multiset permutation"},{"word":"Eulerian polynomial"},{"word":"real-rooted polynomial"},{"word":"alternatingly increasing"},{"word":"self-interlacing"},{"word":"gamma positivity"},{"word":"Ehrhart theory"}],"section":"Research Articles","is_remote":true,"remote_url":"https://escholarship.org/uc/item/135937h5","frozenauthors":[{"first_name":"Danai","middle_name":"","last_name":"Deligeorgaki","name_suffix":"","institution":"Department of Mathematics and Computer Science, Universitat de Barcelona, Barcelona, Spain","department":""},{"first_name":"Bin","middle_name":"","last_name":"Han","name_suffix":"","institution":"Department of Obstetrics and Gynecology, Sahlgrenska Academy, University of Gothenburg, Gothenburg, Sweden","department":""},{"first_name":"Liam","middle_name":"","last_name":"Solus","name_suffix":"","institution":"Department of Mathematics, KTH, Stockholm, Sweden","department":""}],"date_submitted":"2026-04-20T19:28:18Z","date_accepted":"2026-04-20T19:28:18Z","date_published":"2026-04-20T07:00:00Z","render_galley":null,"galleys":[{"label":"","type":"pdf","path":"https://journalpub.escholarship.org/combinatorial_theory/article/65040/galley/49850/download/"}]}