{"pk":65005,"title":"The Newton polytope of the Kronecker product","subtitle":null,"abstract":"We study the Kronecker product of two Schur functions \\(s_\\lambda\\ast s_\\mu\\), defined as the image of the characteristic map of the product of two \\(S_n\\) irreducible characters. We prove special cases of a conjecture of Monical-Tokcan-Yong that its monomial expansion has a saturated Newton polytope. Our proofs employ the Horn inequalities for positivity of Littlewood-Richardson coefficients and imply necessary conditions for the positivity of Kronecker coefficients.\n \nMathematics Subject Classifications: 05E10, 20C30\n \nKeywords: Kronecker coefficients, saturated Newton polytope, symmetric group representations","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":"Kronecker coefficients"},{"word":"saturated Newton polytope"},{"word":"symmetric group representations"}],"section":"Research Articles","is_remote":true,"remote_url":"https://escholarship.org/uc/item/9dq590m9","frozenauthors":[{"first_name":"Greta","middle_name":"","last_name":"Panova","name_suffix":"","institution":"Department of Mathematics, University of Southern California, Los Angeles, California, U.S.A.","department":""},{"first_name":"Chenchen","middle_name":"","last_name":"Zhao","name_suffix":"","institution":"Department of Mathematics, University of California, Davis, California, U.S.A.","department":""}],"date_submitted":"2025-09-12T12:03:50Z","date_accepted":"2025-09-12T12:03:50Z","date_published":"2025-09-15T07:00:00Z","render_galley":null,"galleys":[{"label":"","type":"pdf","path":"https://journalpub.escholarship.org/combinatorial_theory/article/65005/galley/49815/download/"}]}