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A190291
Number of intervals in the weak (Bruhat) order of the symmetric group S_n that are distributive lattices.
0
1, 3, 16, 124, 1262, 15898, 238572, 4152172
OFFSET
1,2
COMMENTS
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.
LINKS
J. R. Stembridge, On the Fully Commutative Elements of Coxeter Groups, Journal of Algebraic Combinatorics, 5 (1996), 353-385.
EXAMPLE
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.
CROSSREFS
Cf. A007767.
Sequence in context: A159607 A087018 A005119 * A090135 A351423 A188417
KEYWORD
nonn,more
AUTHOR
Richard Stanley, May 07 2011
STATUS
approved