## SAGE multiplicity code

Download the SAGE multiplicity code and use it from SAGE with the command

```
load "/path/to/mult_functions.sage"
```

### example usage

To calculate `d_{\L_1,\L_2}`

in Appendix Section A.1 of *Diagonal
free field matrix correlators, global symmetries and giant
gravitons*

```
for part_n in Partitions(5):
for part_k in Partitions(3):
print part_n, part_k, multiplicity(part_n,part_k)
```

To calculate inner products `C(R,R,\L_1)`

, i.e. the number of times
`\L_1`

appears in the symmetric group tensor product `R \otimes R`

,
for `\L_1 = [4,2]`

```
for R in Partitions(6):
print R, inner(R,R,[4,2])
```