Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Combinatorial Properties of Rogers-Ramanujan-Type Identities Arising
  from Hall-Littlewood Polynomials   Here we consider the $q$-series coming from the Hall-Littlewood polynomials,
\begin{equation*} R_\nu(a,b;q)=\sum_{\substack{\lambda \\[1pt] \lambda_1\leq
a}} q^{c|\lambda|} P_{2\lambda}\big(1,q,q^2,\dots;q^{2b+d}\big).
\end{equation*} These series were defined by Griffin, Ono, and Warnaar in their
work on the framework of the Rogers-Ramanujan identities. We devise a recursive
method for computing the coefficients of these series when they arise within
the Rogers-Ramanujan framework. Furthermore, we study the congruence properties
of certain quotients and products of these series, generalizing the famous
Ramanujan congruence \begin{equation*} p(5n+4)\equiv0\pmod{5}. \end{equation*}

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The categories of this paper are: q-bio
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The categories of this paper are: chem-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: math-ph
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The categories of this paper are: adap-org
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-fin
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The categories of this paper are: cs
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The categories of this paper are: cond-mat
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The categories of this paper are: plasm-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: nlin
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The categories of this paper are: alg-geom
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The categories of this paper are: nucl-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-ph