

A190291


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


0




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.


REFERENCES

J.R. Stembridge, On the Fully Commutative Elements of Coxeter Groups, Journal of Algebraic Combinatorics, 5 (1996), 353385.


LINKS

Table of n, a(n) for n=1..8.


EXAMPLE

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


CROSSREFS

Sequence in context: A159607 A087018 A005119 * A090135 A351423 A188417
Adjacent sequences: A190288 A190289 A190290 * A190292 A190293 A190294


KEYWORD

nonn,more


AUTHOR

Richard Stanley, May 07 2011


STATUS

approved



