Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Pattern avoidance of $[4,k]$-pairs in circular permutations   The study of pattern avoidance in linear permutations has been an active area
of research for almost half a century now, starting with the work of Knuth in
1973. More recently, the question of pattern avoidance in circular permutations
has gained significant attention. In 2002-03, Callan and Vella independently
characterized circular permutations avoiding a single permutation of size $4$.
Building on their results, Domagalski et al. studied circular pattern avoidance
for multiple patterns of size $4$. In this article, our main aim is to study
circular pattern avoidance of $[4,k]$-pairs, i.e., circular permutations
avoiding one pattern of size 4 and another of size $k$. We do this by using
well-studied combinatorial objects to represent circular permutations avoiding
a single pattern of size $4$. In particular, we obtain upper bounds for the
number of Wilf equivalence classes of $[4,k]$-pairs. Moreover, we prove that
the obtained bound is tight when the pattern of size $4$ in consideration is
$[1342]$. Using ideas from our general results, we also obtain a complete
characterization of the avoidance classes for $[4,5]$-pairs.

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The categories of this paper are: cond-mat
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The categories of this paper are: astro-ph
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The categories of this paper are: supr-con
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The categories of this paper are: plasm-ph
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The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: physics
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The categories of this paper are: q-fin
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The categories of this paper are: q-bio
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The categories of this paper are: patt-sol
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-th
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The categories of this paper are: econ
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The categories of this paper are: eess
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The categories of this paper are: hep-lat