{"pk":64919,"title":"A symmetric function lift of torus link homology","subtitle":null,"abstract":"Suppose \\(M\\) and \\(N\\) are positive integers and let \\(k = \\gcd(M, N)\\), \\(m = M/k\\), and \\(n=N/k\\). We define a symmetric function \\(L_{M,N}\\) as a weighted sum over certain tuples of lattice paths. We show that \\(L_{M,N}\\) satisfies a generalization of Hogancamp and Mellit's recursion for the triply-graded Khovanov-Rozansky homology of the \\(M,N\\)-torus link. As a corollary, we obtain the triply-graded Khovanov-Rozansky homology of the \\(M,N\\)-torus link as a specialization of \\(L_{M,N}\\). We conjecture that \\(L_{M,N}\\) is equal (up to a constant) to the elliptic Hall algebra operator \\(\\mathbf{Q}_{m,n}\\) composed \\(k\\) times and applied to 1.\n \nMathematics Subject Classifications: 05E05, 57M27\n \nKeywords: Lattice paths, Dyck paths, link homology, torus links, elliptic Hall algebra, LLT polynomials","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 paths"},{"word":"Dyck paths"},{"word":"link homology"},{"word":"torus links"},{"word":"elliptic Hall algebra"},{"word":"LLT polynomials"}],"section":"Research Articles","is_remote":true,"remote_url":"https://escholarship.org/uc/item/9km9594f","frozenauthors":[{"first_name":"Andy","middle_name":"","last_name":"Wilson","name_suffix":"","institution":"Department of Mathematics, Kennesaw State University, Marietta, GA, U.S.A.","department":""}],"date_submitted":"2023-12-22T14:11:56Z","date_accepted":"2023-12-22T14:11:56Z","date_published":"2023-12-22T08:00:00Z","render_galley":null,"galleys":[{"label":"","type":"pdf","path":"https://journalpub.escholarship.org/combinatorial_theory/article/64919/galley/49729/download/"}]}