Geodesic
On counting double centralizers of symmetric groups
Zhipeng Lu1
1Shenzhen MSU-BIT University
The electronic journal of combinatorics, Tome 30 (2023) no. 2
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Let $S_{2m}$ be symmetric group, $h_0=(1\ 2)\cdots(2m-1\ 2m)$ and $H=C(h_0)$. We clarify the structure of $gHg^{-1}\cap H, g\in S_{2m}$, and using tools from analytic combinatorics we prove that the permutations $g$ such that $|gHg^{-1}\cap H|$ bounded by $m^{O(1)}$ have density zero.
DOI : 10.37236/11158
Classification : 20B30, 20C30, 05A16, 20D60
Mots-clés : centralizers, symmetric group

Zhipeng Lu  1

1 Shenzhen MSU-BIT University 
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     author = {Zhipeng Lu},
     title = {On counting double centralizers of symmetric groups},
     journal = {The electronic journal of combinatorics},
     year = {2023},
     volume = {30},
     number = {2},
     doi = {10.37236/11158},
     zbl = {1522.20019},
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Zhipeng Lu. On counting double centralizers of symmetric groups. The electronic journal of combinatorics, Tome 30 (2023) no. 2. doi: 10.37236/11158

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