Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Beck-type companion identities for Franklin's identity   The original Beck conjecture, now a theorem due to Andrews, states that the
difference in the number of parts in all partitions into odd parts and the
number of parts in all strict partitions is equal to the number of partitions
whose set of even parts has one element, and also to the number of partitions
with exactly one part repeated. This is a companion identity to Euler's
identity. The theorem has been generalized by Yang to a companion identity to
Glaisher's identity. Franklin generalized Glaisher's identity, and in this
article, we provide a Beck-type companion identity to Franklin's identity and
prove it both analytically and combinatorially. Andrews' and Yang's respective
theorems fit naturally into this very general frame. We also discuss a
generalization to Franklin's identity of the second Beck-type companion
identity proved by Andrews and Yang in their respective work.

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The categories of this paper are: gr-qc
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The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: funct-an
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The categories of this paper are: ao-sci
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The categories of this paper are: atom-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-alg
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The categories of this paper are: bayes-an
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The categories of this paper are: nucl-th
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The categories of this paper are: adap-org
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The categories of this paper are: quant-ph
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The categories of this paper are: solv-int
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The categories of this paper are: q-fin
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The categories of this paper are: supr-con
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The categories of this paper are: acc-phys