A263485 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give

A263485

Triangle read by rows: T(n,k) (n>=2, 1<=k<=n!) is the number of permutations pi of n such that there are k permutations >= pi in the (strong) Bruhat order.

1, 1, 1, 2, 0, 2, 0, 1, 1, 3, 0, 5, 0, 2, 0, 4, 0, 0, 0, 4, 0, 1, 0, 0, 0, 2, 0, 1, 0, 0, 0, 1, 1, 4, 0, 9, 0, 3, 0, 12, 0, 0, 0, 10, 0, 2, 0, 8, 0, 4, 0, 2, 0, 0, 0, 14, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 10, 0, 0, 0, 4, 0, 0, 0, 2, 0, 2, 0, 4, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 1

(list; graph; refs; listen; history; text; internal format)

OFFSET

2,4

COMMENTS

Row sums give A000142, n >= 2.

By symmetry, this is also the number of permutations of n the number of permutations pi of n such that there are k permutations <= pi in the (strong) Bruhat order.

LINKS

Table of n, a(n) for n=2..101.

FindStat - Combinatorial Statistic Finder, The number of permutations greater than or equal to the given permutation in (strong) Bruhat order, The number of permutations smaller than or equal to the given permutation in (strong) Bruhat order.

Wikipedia, Bruhat order

EXAMPLE

Triangle begins:

1,1,

1,2,0,2,0,1,

1,3,0,5,0,2,0,4,0,0,0,4,0,1,0,0,0,2,0,1,0,0,0,1,

...

CROSSREFS

Cf. A000142.