Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Pattern avoidance in ordered set partitions and words   We consider the enumeration of ordered set partitions avoiding a permutation
pattern, as introduced by Godbole, Goyt, Herdan and Pudwell. Let $\op_{n,k}(p)$
be the number of ordered set partitions of $\{1,2,\ldots,n\}$ into $k$ blocks
that avoid a permutation pattern $p$. We establish an explicit identity between
the number $\op_{n,k}(p)$ and the numbers of words avoiding the inverse of $p$.
This identity allows us to easily translate results on pattern-avoiding words
obtained in earlier works into equivalent results on pattern-avoiding ordered
set partitions. In particular, \emph{(a)} we determine the asymptotic growth
rate of the sequence $(\op_{n,k}(p))_{n\geq 1}$ for every positive $k$ and
every permutation pattern $p$, \emph{(b)} we partially confirm a conjecture of
Godbole et al. concerning the variation of the sequences $(\op_{n,k}p))_{1\leq
k\leq n}$, \emph{(c)} we undertake a detailed study of the number of ordered
set partitions avoiding a pattern of length 3.

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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: comp-gas
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The categories of this paper are: nucl-ex
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The categories of this paper are: adap-org
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The categories of this paper are: solv-int
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The categories of this paper are: ao-sci
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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: stat
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-ph
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The categories of this paper are: hep-th
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The categories of this paper are: supr-con
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The categories of this paper are: gr-qc
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The categories of this paper are: patt-sol