Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Generalized Frobenius partitions, Motzkin paths, and Jacobi forms   We show how Andrews' generating functions for generalized Frobenius
partitions can be understood within the theory of Eichler and Zagier as
specific coefficients of certain Jacobi forms. This reformulation leads to a
recursive process which yields explicit formulas for the generalized Frobenius
partition generating functions in terms of infinite $q$-products. In
particular, we show that specific examples of our result easily reestablish
previously known formulas, and we describe new congruences, both conjectural
and proven, in additional cases. The modular structure of Jacobi forms
indicates that \emph{all} of the coefficients of the forms are of interest. We
give a combinatorial definition of these "companion series" and explore their
combinatorics via the counting of Motzkin paths.

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The categories of this paper are: chem-ph
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The categories of this paper are: q-bio
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The categories of this paper are: ao-sci
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The categories of this paper are: cs
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The categories of this paper are: adap-org
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The categories of this paper are: nucl-th
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The categories of this paper are: solv-int
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The categories of this paper are: math-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: plasm-ph
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The categories of this paper are: stat
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The categories of this paper are: acc-phys
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The categories of this paper are: cond-mat
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The categories of this paper are: quant-ph
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The categories of this paper are: supr-con
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The categories of this paper are: nucl-ex