  Commutative Yang-Mills theories in 1+1 dimensions exhibit an interesting
interplay between geometrical properties and U(N) gauge structures: in the
exact expression of a Wilson loop with $n$ windings a non trivial scaling
intertwines $n$ and $N$. In the non-commutative case the interplay becomes
tighter owing to the merging of space-time and ``internal'' symmetries in a
larger gauge group $U(\infty)$. We perform an explicit perturbative calculation
of such a loop up to ${\cal O}(g^6)$; rather surprisingly, we find that in the
contribution from the crossed graphs (the genuine non-commutative terms) the
scaling we mentioned occurs for large $n$ and $N$ in the limit of maximal
non-commutativity $\theta=\infty$. We present arguments in favour of the
persistence of such a scaling at any perturbative order and succeed in summing
the related perturbative series.
