A263408 - OEIS

A263408

Triangle read by rows: T(n>=1, k>=0) is the number of standard tableaux of size n and (Haglund and Stevens) inversion number k.

1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 4, 4, 3, 2, 1, 1

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OFFSET

1,10

COMMENTS

Row sums give A000085, n >= 2.

The inversion number is the total number of inversion pairs for the tableau. An inversion pair is defined as a pair of cells (a,b), (x,y) such that the content of (x,y) is greater than the content of (a,b) and (x,y) is north of the inversion path of (a,b).

LINKS

Table of n, a(n) for n=1..18.

FindStat - Combinatorial Statistic Finder, The inversion number of a standard tableau as defined by Haglund and Stevens.

J. Haglund and L. Stevens, An extension of the Foata map to standard Young tableaux, Séminaire Lotharingien de Combinatoire 56 (2006), Article B56c.

EXAMPLE

Triangle begins:

1,1,

1,1,1,1,

1,1,2,3,4,4,4,3,2,1,1,

...

CROSSREFS

Cf. A000085.