# FlagSOS.jl

A julia package for extremal combinatorics based on the flag algebra method and its variants. The package offers various hierarchies to compute lower bounds for problems of the form

$$ \begin{aligned} \inf_M\enspace & F(M)\ \text{s.t. }& G_i(M) \geq 0 \quad\text{ for }i=1,\dots,k,\ & H_i(M) = 0 \quad\text{ for }i = 1,\dots, \ell, \end{aligned} $$

where $F$, $G_i$, $H_i$ are quantum flags (linear combinations of sub-model density functions), and $M$ is a model of fixed size or a converging sequence in a given theory. The constraints can include labels, but then the entire $S_n$ orbit needs to be included.

Check out the documentation for details.

## Citing

See `CITATION.bib`

for the relevant reference(s).