Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dominance phenomena: mutation, scattering and cluster algebras   An exchange matrix $B$ dominates an exchange matrix $B'$ if the signs of
corresponding entries weakly agree, with the entry of $B$ always having weakly
greater absolute value. When $B$ dominates $B'$, interesting things happen in
many cases (but not always): the identity map between the associated
mutation-linear structures is often mutation-linear; the mutation fan for $B$
often refines the mutation fan for $B'$; the scattering (diagram) fan for $B$
often refines the scattering fan for $B'$; and there is often an injective
homomorphism from the principal-coefficients cluster algebra for $B'$ to the
principal-coefficients cluster algebra for $B$, preserving $\mathbf{g}$-vectors
and sending the set of cluster variables for $B'$ (or an analogous larger set)
into the set of cluster variables for $B$ (or an analogous larger set). The
scope of the description "often" is not the same in all four contexts and is
not settled in any of them. In this paper, we prove theorems that provide
examples of these dominance phenomena.

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The categories of this paper are: hep-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: dg-ga
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-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
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The categories of this paper are: econ
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The categories of this paper are: bayes-an
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The categories of this paper are: alg-geom
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The categories of this paper are: ao-sci
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The categories of this paper are: funct-an
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The categories of this paper are: q-alg
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The categories of this paper are: cond-mat
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-lat