  This paper presents an algorithm to construct a weighted adjacency matrix of
a plane bipartite graph obtained from a pretzel knot diagram. The determinant
of this matrix after evaluation is shown to be the Jones polynomial of the
pretzel knot by way of perfect matchings (or dimers) of this graph. The weights
are Tutte's activity letters that arise because the Jones polynomial is a
specialization of the signed version of the Tutte polynomial. The relationship
is formalized between the familiar spanning tree setting for the Tait graph and
the perfect matchings of the plane bipartite graph above. Evaluations of these
activity words are related to the chain complex for the Champanerkar-Kofman
spanning tree model of reduced Khovanov homology.
