# 71.38 InverseLittlewoodRichardsonRule

`InverseLittlewoodRichardsonRule(tau)`

Returns a list of all pairs of partitions [mu,nu] such that the Littlewood-Richardson coefficient a_{munu}^tau is non-zero (see LittlewoodRichardsonRule). The list returned is unordered and [mu,nu] will appear a_{munu}^tau times in it.

```gap> InverseLittlewoodRichardsonRule([3,2,1]);
[ [ [  ],[ 3, 2, 1 ] ],[ [ 1 ],[ 3, 2 ] ],[ [ 1 ],[ 2, 2, 1 ] ],
[ [ 1 ],[ 3, 1, 1 ] ],[ [ 1, 1 ],[ 2, 2 ] ],[ [ 1, 1 ],[ 3, 1 ] ],
[ [ 1, 1 ],[ 2, 1, 1 ] ],[ [ 1, 1, 1 ],[ 2, 1 ] ],[ [ 2 ],[ 2, 2 ] ],
[ [ 2 ],[ 3, 1 ] ],[ [ 2 ],[ 2, 1, 1 ] ],[ [ 2, 1 ],[ 3 ] ],
[ [ 2, 1 ],[ 2, 1 ] ],[ [ 2, 1 ],[ 2, 1 ] ],[ [ 2, 1 ],[ 1, 1, 1 ] ],
[ [ 2, 1, 1 ],[ 2 ] ],[ [ 2, 1, 1 ],[ 1, 1 ] ],[ [ 2, 2 ],[ 2 ] ],
[ [ 2, 2 ],[ 1, 1 ] ],[ [ 2, 2, 1 ],[ 1 ] ],[ [ 3 ],[ 2, 1 ] ],
[ [ 3, 1 ],[ 2 ] ],[ [ 3, 1 ],[ 1, 1 ] ],[ [ 3, 1, 1 ],[ 1 ] ],
[ [ 3, 2 ],[ 1 ] ],[ [ 3, 2, 1 ],[ ] ] ]
```

See also `LittlewoodRichardsonRule` LittlewoodRichardsonRule.

This function requires the package ``specht'' (see RequirePackage).

GAP 3.4.4
April 1997