Young Tableau
The Young Tableau of a Young Diagram is obtained by placing the numbers 1, ..., 
in the boxes of thediagram. A ``standard'' Young tableau is a Young tableau in which the numbers form a nondecreasing sequence along each lineand 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 RecurrenceRelation
with
and 
.There is a correspondence between a Permutation and a pair of Young tableaux, known as the SchenstedCorrespondence. The number of all standard Young tableaux with a given shape (corresponding to a given YoungDiagram) is calculated with the Hook Length Formula. The Bumping Algorithm is used to construct a standardYoung 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. SequenceA000085/M1221in ``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.
- Pasch's Theorem
- Pass Equivalent
- Pass Move
- Patch
- Path
- Path Graph
- Path Integral
- Pathwise-Connected
- Patriarchal Cross
- Pauli Matrices
- Pauli Spin Matrices
- Payoff Matrix
- P-Circle
- Peacock's Tail
- Peano Arithmetic
- Peano Curve
- Peano-Gosper Curve
- Peano's Axioms
- Peano Surface
- Pear Curve
- Pearls of Sluze
- Pear-Shaped Curve
- Pearson-Cunningham Function
- Pearson Kurtosis
- Pearson Mode Skewness