2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/63472It 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.AMS-LaTeX, 13 pages with 12 figuresGeometric TopologyQuantum Algebratext