Geodesic
Counting parabolic double cosets in symmetric groups
Thomas Browning1
1University of Washington
The electronic journal of combinatorics, Tome 28 (2021) no. 3
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Billey, Konvalinka, Petersen, Solfstra, and Tenner recently presented a method for counting parabolic double cosets in Coxeter groups, and used it to compute $p_n$, the number of parabolic double cosets in $S_n$, for $n\leq13$. In this paper, we derive a new formula for $p_n$ and an efficient polynomial time algorithm for evaluating this formula. We use these results to compute $p_n$ for $n\leq5000$ and to prove an asymptotic formula for $p_n$ that was conjectured by Billey et al.
DOI : 10.37236/9988
Classification : 20F55, 05A15, 05A16

Thomas Browning  1

1 University of Washington 
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     author = {Thomas Browning},
     title = {Counting parabolic double cosets in symmetric groups},
     journal = {The electronic journal of combinatorics},
     year = {2021},
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     number = {3},
     doi = {10.37236/9988},
     zbl = {1542.20162},
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Thomas Browning. Counting parabolic double cosets in symmetric groups. The electronic journal of combinatorics, Tome 28 (2021) no. 3. doi: 10.37236/9988

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