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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 (list; graph; refs; listen; history; text; internal format)
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), 353-385.

LINKS

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

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

Sequence in context: A159607 A087018 A005119 * A090135 A188417 A157457

Adjacent sequences:  A190288 A190289 A190290 * A190292 A190293 A190294

KEYWORD

nonn,more

AUTHOR

Richard Stanley, May 07 2011

STATUS

approved

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Last modified May 19 08:25 EDT 2019. Contains 323389 sequences. (Running on oeis4.)