Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dirichlet-Poincar\'{e} profiles of graphs and groups   We define Poincar\'{e} profiles of Dirichlet type for graphs of bounded
degree, in analogy with the Poincar\'{e} profiles (of Neumann type) defined in
[HMT19]. The obvious first definition yields nothing of interest, but an
alternative definition yields a spectrum of profiles which are quasi-isometry
invariants and monotone with respect to subgroup inclusion. Moreover, in the
extremal cases $p=1$ and $p=\infty$, they detect the F\o lner function and the
growth function respectively.

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The categories of this paper are: q-bio
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The categories of this paper are: cond-mat
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The categories of this paper are: astro-ph
15
The categories of this paper are: nucl-ex
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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: econ
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The categories of this paper are: nlin
3
The categories of this paper are: physics
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-ex
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The categories of this paper are: plasm-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-ph
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The categories of this paper are: funct-an
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The categories of this paper are: quant-ph