  It can be conjectured that the colored Jones function of a knot can be
computed in terms of counting paths on the graph of a planar projection of a
knot. On the combinatorial level, the colored Jones function can be replaced by
its weight system. We give two curious formulas for the weight system of a
colored Jones function: one in terms of the permanent of a matrix associated to
a chord diagram, and another in terms of counting paths of intersecting chords.
