Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Eulerian distribution on involutions is indeed $\gamma$-positive   Let $\mathcal I_n$ and $\mathcal J_n$ denote the set of involutions and
fixed-point free involutions of $\{1, \dots, n\}$, respectively, and let
$\text{des}(\pi)$ denote the number of descents of the permutation $\pi$. We
prove a conjecture of Guo and Zeng which states that $I_n(t) := \sum_{\pi \in
\mathcal I_n} t^{\text{des}(\pi)}$ is $\gamma$-positive for $n \ge 1$ and
$J_{2n}(t) := \sum_{\pi \in \mathcal J_{2n}} t^{\text{des}(\pi)}$ is
$\gamma$-positive for $n \ge 9$. We also prove that the number of $(3412,
3421)$-avoiding permutations with $m$ double descents and $k$ descents is equal
to the number of separable permutations with $m$ double descents and $k$
descents.

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The categories of this paper are: atom-ph
16
The categories of this paper are: stat
18
The categories of this paper are: econ
14
The categories of this paper are: math-ph
23
The categories of this paper are: solv-int
12
The categories of this paper are: nucl-th
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The categories of this paper are: comp-gas
13
The categories of this paper are: quant-ph
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The categories of this paper are: q-fin
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The categories of this paper are: hep-lat
9
The categories of this paper are: nlin
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The categories of this paper are: ao-sci
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The categories of this paper are: eess
7
The categories of this paper are: hep-th
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The categories of this paper are: alg-geom
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The categories of this paper are: chao-dyn