A263485 - OEIS

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

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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.