Let $\Gamma_{g,b}^m$ denote the mapping class group of a genus $g$ surface with $b$ non-permutable parametrised boundary curves and $m$ permutable punctures.

It is clear that in general, presentations for these groups are hard. I only need for the general case a set of generators (I want to show that two morphisms $\varphi,\psi:\Gamma\to G$ are equal and I want to check this on the generators). Partial answers are the following:

- If $b,m=0$ (so we have a closed surface), then the group is generated by Dehn twists which can be easily drawn on the surface.
- If $g,m=0$, we can declare one boundary curve as “outer” and the group is generated by Dehn twists along the inner boundary curves and the pure braid generators $\alpha_{ij}$.

From Farb–Margalit, I know that there are always finitely many Dehn twists (or half twists) which generate $\Gamma$, but can we say in general where they are?