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Creators/Authors contains: "Folsom, Amanda"

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  1. ( , 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 
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    Free, publicly-accessible full text available February 15, 2025
  2. ; ; ; ; ( , Research in the Mathematical Sciences)
    Free, publicly-accessible full text available December 1, 2024
  3. ; ; ( , The Ramanujan journal)
    Using equidistribution criteria, we establish divisibility by cyclotomic polynomials of several partition polynomials of interest, including spt-crank, overpartition pairs, and t-core partitions. As corollaries, we obtain new proofs of various Ramanujan-type congruences for associated partition functions. Moreover, using results of Erdös and Turán, we establish the equidistribution of roots of partition polynomials on the unit circle including those for the rank, crank, spt, and unimodal sequences. Our results complement earlier work on this topic by Stanley, Boyer-Goh, and others. We explain how our methods may be used to establish similar results for other partition polynomials of interest, and offer many related open questions and examples. 
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    Free, publicly-accessible full text available August 1, 2024
  4. ; ; ; ; ( , 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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    Free, publicly-accessible full text available July 17, 2024
  5. ; ; ; ; ; ( , Notices of the American Mathematical Society)
    Free, publicly-accessible full text available June 1, 2024
  6. ; ; ; ; ; ( , Discrete mathematics)
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  7. ; ; ; ( , Research in number theory)
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  8. ( , International Journal of Number Theory)
    null (Ed.)
    In 1920, Ramanujan studied the asymptotic differences between his mock theta functions and modular theta functions, as [Formula: see text] tends towards roots of unity singularities radially from within the unit disk. In 2013, the bounded asymptotic differences predicted by Ramanujan with respect to his mock theta function [Formula: see text] were established by Ono, Rhoades, and the author, as a special case of a more general result, in which they were realized as special values of a quantum modular form. Our results here are threefold: we realize these radial limit differences as special values of a partial theta function, provide full asymptotic expansions for the partial theta function as [Formula: see text] tends towards roots of unity radially, and explicitly evaluate the partial theta function at roots of unity as simple finite sums of roots of unity. 
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  9. ; ; ( , Journal of the Australian Mathematical Society)
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  10. ( , Transactions of the London Mathematical Society)