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

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

Offset: 1

Author

Richard Stanley, May 07 2011

Keywords

• nonn
• more

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.

Examples

			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.
		

Links

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

Crossrefs

Cf. A007767.