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• W3130682847 abstract "Abstract We generalize the shuffle theorem and its $(km,kn)$ version, as conjectured by Haglund et al. and Bergeron et al. and proven by Carlsson and Mellit, and Mellit, respectively. In our version the $(km,kn)$ Dyck paths on the combinatorial side are replaced by lattice paths lying under a line segment whose x and y intercepts need not be integers, and the algebraic side is given either by a Schiffmann algebra operator formula or an equivalent explicit raising operator formula. We derive our combinatorial identity as the polynomial truncation of an identity of infinite series of $operatorname {mathrm {GL}}_{l}$ characters, expressed in terms of infinite series versions of LLT polynomials. The series identity in question follows from a Cauchy identity for nonsymmetric Hall–Littlewood polynomials." @default.
• W3130682847 created "2021-03-01" @default.
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• W3130682847 date "2023-01-01" @default.
• W3130682847 modified "2023-10-18" @default.
• W3130682847 title "A Shuffle Theorem for Paths Under Any Line" @default.
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• W3130682847 doi "https://doi.org/10.1017/fmp.2023.4" @default.
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