Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Unary Patterns of Size Four with Morphic Permutations   We investigate the avoidability of unary patterns of size of four with
morphic permutations. More precisely, we show that, for the positive integers
$i,j,k$, the sizes of the alphabets over which a pattern $x \pi ^ {i} (x)
\pi^{j}(x) \pi^{k}(x)$ is avoidable are an interval of the integers (where $x$
is a word variable and $\pi$ is a function variable with values in the set of
all morphic permutations of the respective alphabets). We also show how to
compute a good approximation of this interval. This continues the work of
[Manea et al., 2015], where a complete characterisation of the avoidability of
cubic patterns with permutations was given.

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The categories of this paper are: hep-th
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The categories of this paper are: nlin
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The categories of this paper are: quant-ph
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The categories of this paper are: solv-int
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The categories of this paper are: adap-org
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The categories of this paper are: hep-ph
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The categories of this paper are: stat
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The categories of this paper are: gr-qc
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The categories of this paper are: chem-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: econ
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The categories of this paper are: cond-mat
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The categories of this paper are: physics
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The categories of this paper are: alg-geom
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The categories of this paper are: dg-ga
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The categories of this paper are: astro-ph