OFFSET
1,2
COMMENTS
This is closely related to the number of contingency tables on n elements (see A120733), but many contingency tables correspond to the same parabolic double coset, e.g., for n=2, there are 5 contingency tables, but only 3 distinct cosets.
LINKS
Thomas Browning, Table of n, a(n) for n = 1..400
Sara Billey, Matjaz Konvalinka, T. Kyle Petersen, William Slofstra, and Bridget Tenner, Parabolic double cosets in Coxeter groups, Discrete Mathematics and Theoretical Computer Science, Submitted, 2016.
Sara Billey, Matjaz Konvalinka, T. Kyle Petersen, William Slofstra, and Bridget Tenner, Parabolic double cosets in Coxeter groups, Electron. J. Combin., Volume 25, Issue 1 (2018) P1.23.
Thomas Browning, Counting Parabolic Double Cosets in Symmetric Groups, arXiv:2010.13256 [math.CO], 2020.
Masato Kobayashi, Construction of double coset system of a Coxeter group and its applications to Bruhat graphs, arXiv:1907.11801 [math.CO], 2019.
FORMULA
a(n) is asymptotic to n! / (2^(log(2)/2 + 2) * log(2)^(2*n + 2)). [Conjectured Vaclav Kotesovec Sep 08 2020, proved Thomas Browning Oct 26 2020]
EXAMPLE
For n=2, there are three parabolic double cosets: {12}, {21}, and {12, 21}.
CROSSREFS
KEYWORD
nonn
AUTHOR
Kyle Petersen, Nov 16 2015
EXTENSIONS
More terms from Thomas Browning, Sep 07 2020
STATUS
approved