Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Positional Marked Patterns in Permutations   We define and study positional marked patterns, permutations $\tau$ where one
of elements in $\tau$ is underlined. Given a permutation $\sigma$, we say that
$\sigma$ has a $\tau$-match at position $i$ if $\tau$ occurs in $\sigma$ in
such a way that $\sigma_i$ plays the role of the underlined element in the
occurrence. We let $pmp_\tau(\sigma)$ denote the number of positions $i$ which
$\sigma$ has a $\tau$-match. This defines a new class of statistics on
permutations, where we study such statistics and prove a number of results. In
particular, we prove that two positional marked patterns $1\underline{2}3$ and
$1\underline{3}2$ give rise to two statistics that have the same distribution.
The equidistibution phenomenon also occurs in other several collections of
patterns like $\left \{1\underline{2}3 , 1\underline{3}2 \right \}$, and $\left
\{ 1\underline234, 1\underline243, \underline2134, \underline2 1 4 3 \right
\}$, as well as two positional marked patterns of any length $n$: $\left \{
1\underline 2\tau , \underline 21\tau \right \}$.

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The categories of this paper are: hep-th
37
The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th
14
The categories of this paper are: math-ph
3
The categories of this paper are: physics
34
The categories of this paper are: chem-ph
16
The categories of this paper are: stat
30
The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex
12
The categories of this paper are: nucl-th
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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: quant-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: comp-gas
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The categories of this paper are: atom-ph