Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Acyclicity in finite groups and groupoids   We expound a concise construction of finite groups and groupoids whose Cayley
graphs satisfy graded acyclicity requirements. Our acyclicity criteria concern
cyclic patterns formed by coset-like configurations w.r.t. subsets of the
generator set rather than just by individual generators. The proposed
constructions correspondingly yield finite groups and groupoids whose Cayley
graphs satisfy much stronger acyclicity conditions than large girth. We thus
obtain generic and canonical constructions of highly homogeneous graph
structures with strong acyclicity properties, which support known applications
in finite graph and hypergraph coverings that locally unfold cyclic
configurations. with involutive generators, with the additional benefit of a
more uniform approach across these settings.

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The categories of this paper are: physics
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The categories of this paper are: econ
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The categories of this paper are: dg-ga
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The categories of this paper are: comp-gas
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-ex
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The categories of this paper are: astro-ph
36
The categories of this paper are: cmp-lg
34
The categories of this paper are: chem-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: q-alg
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The categories of this paper are: supr-con
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The categories of this paper are: eess
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The categories of this paper are: alg-geom
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The categories of this paper are: mtrl-th
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The categories of this paper are: quant-ph