Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A principle for converting Lindstr\"om-type lemmas to Stembridge-type
  theorems, with applications to walks, groves, and alternating flows   We prove that Fomin's generalization of Lindstr\"om's lemma for paths on
acyclic directed graphs to walks on general directed graphs also generalizes a
theorem of Stembridge in the same way. Moreover, we show that whenever a family
of operations satisfies a Lindstr\"om-type determinant relation, a related
family of operations satisfies a Stembridge-type Pfaffian relation. We give
example applications to Kenyon and Wilson's work on groves and to Talaska's
work on alternating flows.

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The categories of this paper are: adap-org
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The categories of this paper are: gr-qc
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The categories of this paper are: bayes-an
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The categories of this paper are: supr-con
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The categories of this paper are: cs
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The categories of this paper are: math-ph
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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: eess
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-ex
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The categories of this paper are: ao-sci
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The categories of this paper are: physics
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The categories of this paper are: nucl-ex
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The categories of this paper are: solv-int
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The categories of this paper are: q-fin