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Award ID contains: 2200728

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  1. ; ; ; (, Symmetry, Integrability and Geometry: Methods and Applications)
    We study the zero set of polynomials built from partition statistics, complementing earlier work in this direction by Boyer, Goh, Parry, and others. In particular, addressing a question of Males with two of the authors, we prove asymptotics for the values of $$t$$-hook polynomials away from an annulus and isolated zeros of a theta function. We also discuss some open problems and present data on other polynomial families, including those associated to deformations of Rogers-Ramanujan functions. 
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    Free, publicly-accessible full text available April 21, 2026
  2. ; (, Research in the Mathematical Sciences)
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  3. (, Journal of Mathematical Analysis and Applications)
    We prove that general two-variable partial theta functions with periodic coefficients are quantum Jacobi forms, and establish their explicit transformation and analytic properties. As applications, we also prove that seven infinite families of q-hypergeometric multisums and related partial theta functions of interest arising from certain knot colored Jones polynomials, Kashaev invariants for torus knots and Virasoro characters, and “strange” identities, appearing in (separate) works of Bijaoui et al., Hikami, Hikami-Kirillov, Lovejoy, and Zagier are quantum Jacobi forms. 
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  4. ; ; ; ; (, Research in the Mathematical Sciences)
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  5. ; ; ; ; (, Séminaire lotharingien de combinatoire)
    Séminaire Lotharingien de Combinatoire - FPSAC 2023; Proceedings of the 35th International Conference on "Formal Power Series and Algebraic Combinatorics", July 17 - 21, 2023, University of California at Davis, USA; Motivated in part by hook-content formulas for certain restricted partitions in representation theory, we consider the total number of hooks of fixed length in odd versus distinct partitions. We show that there are more hooks of length 2, respectively 3, in all odd partitions of n than in all distinct partitions of n, and make the analogous conjecture for arbitrary hook length t ≥ 2. To this end, we establish very general linear inequalities for the number of distinct partitions, which is also of independent interest. We also establish additional related partition bias results. 
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    Accepted Manuscript Full Text Available
  6. ; ; ; ; ; (, Notices of the American Mathematical Society)
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