Counting parabolic double cosets in symmetric groups (Q2049615)
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scientific article; zbMATH DE number 7387079
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Counting parabolic double cosets in symmetric groups |
scientific article; zbMATH DE number 7387079 |
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Counting parabolic double cosets in symmetric groups (English)
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27 August 2021
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Summary: 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 \(n\leqslant 13\). 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 \(n\leqslant 5000\) and to prove an asymptotic formula for \(p_n\) that was conjectured by Billey et al.
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