The Young Tableau of a Young Diagram is obtained by placing the numbers 1, ..., in the boxes of the
diagram. A ``standard'' Young tableau is a Young tableau in which the numbers form a nondecreasing sequence along each line
and along each column. The standard Young tableaux of size three are given by
,
,
, and
. The number of standard Young tableaux of size 1, 2, 3, ... are 1,
2, 4, 10, 26, 76, 232, 764, 2620, 9496, ... (Sloane's A000085). These numbers can be generated by the Recurrence
Relation

with and .

There is a correspondence between a Permutation and a pair of Young tableaux, known as the Schensted Correspondence. The number of all standard Young tableaux with a given shape (corresponding to a given Young Diagram) is calculated with the Hook Length Formula. The Bumping Algorithm is used to construct a standard Young tableau from a permutation of .

**References**

Fulton, W. *Young Tableaux with Applications to Representation Theory and Geometry.* New York:
Cambridge University Press, 1996.

Ruskey, F. ``Information on Permutations.'' http://sue.csc.uvic.ca/~cos/inf/perm/PermInfo.html#Tableau.

Skiena, S. S. *The Algorithm Design Manual.* New York: Springer-Verlag, pp. 254-255, 1997.

Sloane, N. J. A. Sequence
A000085/M1221
in ``An On-Line Version of the Encyclopedia of Integer Sequences.''
http://www.research.att.com/~njas/sequences/eisonline.html and Sloane, N. J. A. and Plouffe, S.
*The Encyclopedia of Integer Sequences.* San Diego: Academic Press, 1995.

© 1996-9

1999-05-26