# lr_tensor

Compute the tensor project of two Young tableaux

Compute the tensor product of two tableaux or filled tableaux. The
algorithm acts on objects which have the `Tableau`

or `FilledTableau`

property, through which it is possible to
set the dimension. The standard Littlewoord-Richardson algorithm is
used to construct the tableaux in the tensor product. An example
with `Tableau`

objects is given below.\tableau{#}::Tableau(dimension=10).
ex:=\tableau{2}{2} \tableau{2}{2}{1};
lr_tensor(_);

\(\displaystyle{}\)\(\displaystyle \)\(\displaystyle\)

\(\displaystyle{}\)\(\displaystyle+\)\(\displaystyle+\)\(\displaystyle+\)\(\displaystyle+\)\(\displaystyle+\)\(\displaystyle+\)\(\displaystyle+\)\(\displaystyle+\)\(\displaystyle\)

The same example, but now with

`FilledTableau`

objects, is\ftableau{#}::FilledTableau(dimension=10).
ex:=\ftableau{0,0}{1,1} \ftableau{a,a}{b,b};

\(\displaystyle{}\)\(\displaystyle \)\(\displaystyle\)

lr_tensor(_);

\(\displaystyle{}\)\(\displaystyle+\)\(\displaystyle+\)\(\displaystyle+\)\(\displaystyle+\)\(\displaystyle+\)\(\displaystyle\)

ex:=\ftableau{1} \ftableau{2} \ftableau{3} \ftableau{4};

\(\displaystyle{}\)\(\displaystyle \)\(\displaystyle \)\(\displaystyle \)\(\displaystyle\)

converge(ex):
lr_tensor(_)
distribute(_)
;

\(\displaystyle{}\)\(\displaystyle+\)\(\displaystyle+\)\(\displaystyle+\)\(\displaystyle+\)\(\displaystyle+\)\(\displaystyle+\)\(\displaystyle+\)\(\displaystyle+\)\(\displaystyle+\)\(\displaystyle\)