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A190291 Number of intervals in the weak (Bruhat) order of the symmetric group S_n that are distributive lattices. 0

%I

%S 1,3,16,124,1262,15898,238572,4152172

%N Number of intervals in the weak (Bruhat) order of the symmetric group S_n that are distributive lattices.

%C The intervals [u,v] in the weak order that are distributive lattices are characterized by Stembridge. They are the intervals such that u^{-1}.v is fully commutative, i.e. avoids the pattern 321.

%D J.R. Stembridge, On the Fully Commutative Elements of Coxeter Groups, Journal of Algebraic Combinatorics, 5 (1996), 353-385.

%e Example: for n=3 there are six 1-element intervals, six 2-element intervals, and four intervals that are 3-element chains, for a total of 16.

%K nonn,more

%O 1,2

%A _Richard Stanley_, May 07 2011

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Last modified October 5 08:41 EDT 2022. Contains 357252 sequences. (Running on oeis4.)