<s>
In	O
mathematics	O
,	O
the	O
Robinson	B-Algorithm
–	I-Algorithm
Schensted	I-Algorithm
correspondence	I-Algorithm
is	O
a	O
bijective	B-Algorithm
correspondence	O
between	O
permutations	B-Algorithm
and	O
pairs	O
of	O
standard	O
Young	O
tableaux	O
of	O
the	O
same	O
shape	O
.	O
</s>
<s>
The	O
correspondence	O
has	O
been	O
generalized	O
in	O
numerous	O
ways	O
,	O
notably	O
by	O
Knuth	O
to	O
what	O
is	O
known	O
as	O
the	O
Robinson	B-Algorithm
–	I-Algorithm
Schensted	I-Algorithm
–	I-Algorithm
Knuth	I-Algorithm
correspondence	I-Algorithm
,	O
and	O
a	O
further	O
generalization	O
to	O
pictures	O
by	O
Zelevinsky	O
.	O
</s>
<s>
The	O
simplest	O
description	O
of	O
the	O
correspondence	O
is	O
using	O
the	O
Schensted	B-Algorithm
algorithm	I-Algorithm
,	O
a	O
procedure	O
that	O
constructs	O
one	O
tableau	O
by	O
successively	O
inserting	O
the	O
values	O
of	O
the	O
permutation	B-Algorithm
according	O
to	O
a	O
specific	O
rule	O
,	O
while	O
the	O
other	O
tableau	O
records	O
the	O
evolution	O
of	O
the	O
shape	O
during	O
construction	O
.	O
</s>
<s>
The	O
correspondence	O
is	O
often	O
referred	O
to	O
as	O
the	O
Robinson	B-Algorithm
–	I-Algorithm
Schensted	I-Algorithm
algorithm	I-Algorithm
,	O
although	O
the	O
procedure	O
used	O
by	O
Robinson	O
is	O
radically	O
different	O
from	O
the	O
Schensted	B-Algorithm
algorithm	I-Algorithm
,	O
and	O
almost	O
entirely	O
forgotten	O
.	O
</s>
<s>
Other	O
methods	O
of	O
defining	O
the	O
correspondence	O
include	O
a	O
nondeterministic	O
algorithm	O
in	O
terms	O
of	O
jeu	B-Algorithm
de	I-Algorithm
taquin	I-Algorithm
.	O
</s>
<s>
More	O
formally	O
,	O
the	O
following	O
pseudocode	B-Language
describes	O
the	O
row-insertion	O
of	O
a	O
new	O
value	O
into	O
.	O
</s>
<s>
The	O
full	O
Schensted	B-Algorithm
algorithm	I-Algorithm
applied	O
to	O
a	O
permutation	B-Algorithm
proceeds	O
as	O
follows	O
.	O
</s>
<s>
It	O
can	O
be	O
seen	O
that	O
given	O
any	O
pair	O
of	O
standard	O
Young	O
tableaux	O
of	O
the	O
same	O
shape	O
,	O
there	O
is	O
an	O
inverse	O
procedure	O
that	O
produces	O
a	O
permutation	B-Algorithm
that	O
will	O
give	O
rise	O
to	O
by	O
the	O
Schensted	B-Algorithm
algorithm	I-Algorithm
.	O
</s>
<s>
These	O
two	O
inverse	O
algorithms	O
define	O
a	O
bijective	B-Algorithm
correspondence	O
between	O
permutations	B-Algorithm
of	O
on	O
one	O
side	O
,	O
and	O
pairs	O
of	O
standard	O
Young	O
tableaux	O
of	O
equal	O
shape	O
and	O
containing	O
squares	O
on	O
the	O
other	O
side	O
.	O
</s>
<s>
If	O
the	O
Robinson	B-Algorithm
–	I-Algorithm
Schensted	I-Algorithm
correspondence	I-Algorithm
associates	O
tableaux	O
to	O
a	O
permutation	B-Algorithm
,	O
then	O
it	O
associates	O
to	O
the	O
inverse	O
permutation	B-Algorithm
.	O
</s>
<s>
Further	O
properties	O
,	O
all	O
assuming	O
that	O
the	O
correspondence	O
associates	O
tableaux	O
to	O
the	O
permutation	B-Algorithm
.	O
</s>
<s>
In	O
the	O
pair	O
of	O
tableaux	O
associated	O
to	O
the	O
reversed	O
permutation	B-Algorithm
,	O
the	O
tableau	O
is	O
the	O
transpose	O
of	O
the	O
tableau	O
,	O
and	O
is	O
a	O
tableau	O
determined	O
by	O
,	O
independently	O
of	O
(	O
namely	O
the	O
transpose	O
of	O
the	O
tableau	O
obtained	O
from	O
by	O
the	O
Schützenberger	O
involution	B-Algorithm
)	O
.	O
</s>
<s>
If	O
is	O
an	O
involution	B-Algorithm
,	O
then	O
the	O
number	O
of	O
fixed	O
points	O
of	O
equals	O
the	O
number	O
of	O
columns	O
of	O
odd	O
length	O
in	O
.	O
</s>
