<s>
In	O
algebraic	O
combinatorics	O
,	O
a	O
Bender	B-Algorithm
–	I-Algorithm
Knuth	I-Algorithm
involution	I-Algorithm
is	O
an	O
involution	B-Algorithm
on	O
the	O
set	O
of	O
semistandard	O
tableaux	O
,	O
introduced	O
by	O
in	O
their	O
study	O
of	O
plane	O
partitions	O
.	O
</s>
<s>
The	O
Bender	B-Algorithm
–	I-Algorithm
Knuth	I-Algorithm
involutions	I-Algorithm
σk	O
are	O
defined	O
for	O
integers	O
k	O
,	O
and	O
act	O
on	O
the	O
set	O
of	O
semistandard	O
skew	O
Young	O
tableaux	O
of	O
some	O
fixed	O
shape	O
μ/ν	O
,	O
where	O
μ	O
and	O
ν	O
are	O
partitions	O
.	O
</s>
<s>
Bender	B-Algorithm
–	I-Algorithm
Knuth	I-Algorithm
involutions	I-Algorithm
can	O
be	O
used	O
to	O
show	O
that	O
the	O
number	O
of	O
semistandard	O
skew	O
tableaux	O
of	O
given	O
shape	O
and	O
weight	O
is	O
unchanged	O
under	O
permutations	O
of	O
the	O
weight	O
.	O
</s>
<s>
Bender	B-Algorithm
–	I-Algorithm
Knuth	I-Algorithm
involutions	I-Algorithm
were	O
used	O
by	O
to	O
give	O
a	O
short	O
proof	O
of	O
the	O
Littlewood	O
–	O
Richardson	O
rule	O
.	O
</s>
