Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Mutations of reflections and existence of pseudo-acyclic orderings for
  type $A_n$   In a recent paper by K.-H. Lee, K. Lee and M. Mills, a mutation of
reflections in the universal Coxeter group is defined in association with a
mutation of a quiver. A matrix representation of these reflections is
determined by a linear ordering on the set of vertices of the quiver. It was
conjectured that there exists an ordering (called a pseudo-acyclic ordering in
this paper) such that whenever two mutation sequences of a quiver lead to the
same labeled seed, the representations of the associated reflections also
coincide. In this paper, we prove this conjecture for every quiver
mutation-equivalent to an orientation of a type $A_n$ Dynkin diagram by
decomposing a mutation sequence into a product of elementary swaps and checking
relations studied by Barot and Marsh.

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The categories of this paper are: dg-ga
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The categories of this paper are: chao-dyn
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The categories of this paper are: astro-ph
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The categories of this paper are: q-alg
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The categories of this paper are: cmp-lg
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The categories of this paper are: plasm-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: math-ph
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The categories of this paper are: q-bio
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The categories of this paper are: acc-phys
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The categories of this paper are: gr-qc
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The categories of this paper are: solv-int
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The categories of this paper are: hep-ex
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The categories of this paper are: eess
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The categories of this paper are: bayes-an
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The categories of this paper are: q-fin