  We give a simple diagrammatic algorithm for writing the chiral large $N$
expansion of intersecting Wilson loops in $2D$ $SU(N)$ and $U(N) $Yang Mills
theory in terms of symmetric groups, generalizing the result of Gross and
Taylor for partition functions. We prove that these expansions compute Euler
characters of a space of holomorphic maps from string worldsheets with
boundaries. We prove that the Migdal-Makeenko equations hold for the chiral
theory and show that they can be expressed as linear constraints on
perturbations of the chiral $YM2$ partition functions. We briefly discuss
finite $N$ , the non-chiral expansion, and higher dimensional lattice models.
