A263409 Triangle read by rows: T(n>=2, k>=0) is the number of standard tableaux of size n and Shynar inversion number k.

2, 3, 1, 5, 3, 2, 7, 6, 7, 5, 1, 11, 12, 16, 16, 12, 6, 3, 15, 20, 31, 38, 41, 36, 26, 15, 7, 3, 22, 34, 58, 79, 98, 107, 107, 89, 71, 50, 28, 14, 6, 1

Offset

2,1

Comments

Row sums give A000085, n >= 2.

Shynar's inversion number is the number of inversion pairs in a standard Young tableau, where an inversion pair is defined as a pair of integers (x,y) such that y > x and y appears strictly southwest of x in the tableau.

Links

Table of n, a(n) for n=2..43.

FindStat - Combinatorial Statistic Finder, The Shynar inversion number of a standard tableau.

Michael Shynar, On Inversions in Standard Young Tableaux, Formal Power Series and Algebraic Combinatorics, 2004.

Example

Triangle begins:
2,
3,1,
5,3,2,
7,6,7,5,1,
11,12,16,16,12,6,3,
15,20,31,38,41,36,26,15,7,3,
22,34,58,79,98,107,107,89,71,50,28,14,6,1,
...

Crossrefs

Cf. A000085.

Sequence in context: A261555 A134734 A214569 * A047706 A300518 A111609

Adjacent sequences: A263406 A263407 A263408 * A263410 A263411 A263412

Keyword

nonn,tabf,more

Author

Christian Stump, Oct 17 2015

Status

approved