The Young tableau (plural, "tableaux") of a Ferrers 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 an increasing sequence along each line
and along each column. For example, the standard Young tableaux of size are given by , , , and , illustrated above. The bumping
algorithm is used to construct a standard Young tableau from a permutation of
, and the number of standard
Young tableaux of size 1, 2, 3, ... are 1, 2, 4, 10, 26, 76, 232, 764, 2620, 9496,
... (OEIS A000085). These numbers can be generated
by the recurrence relation
with
and .
This is the same as the number of permutation
involutions on
elements (Skiena 1990, p. 32).
The number of all possible standard Young tableaux of a given shape can also be considered, and can be calculated with the hook length formula.
For example, the illustration above shows the 35 standard tableaux of shape .
in the 
boxes of the diagram. A "standard" Young tableau
is a Young tableau in which the numbers form an increasing sequence along each line
and along each column. For example, the standard Young tableaux of size 
are given by 
, 
, 
, and 
, illustrated above. The bumping
algorithm is used to construct a standard Young tableau from a permutation of
, and the number of standard
Young tableaux of size 1, 2, 3, ... are 1, 2, 4, 10, 26, 76, 232, 764, 2620, 9496,
... (OEIS A000085). These numbers can be generated
by the recurrence relation
and 
.
This is the same as the number of permutation
involutions on 
elements (Skiena 1990, p. 32).
.
