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A263409 Triangle read by rows: T(n>=2, k>=0) is the number of standard tableaux of size n and Shynar inversion number k. 0
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified July 29 09:31 EDT 2021. Contains 346344 sequences. (Running on oeis4.)