Transition polynomial as a weight system for binary delta-matroids
To a singular knot K with n double points, one can associate a chord
diagram with n chords. A chord diagram can also be understood as a 4-
regular graph endowed with an oriented Euler circuit. L. Traldi introduced
a polynomial invariant for such graphs, called a transition polynomial.
We specialize this polynomial to a multiplicative weight system, that is,
a function on chord diagrams satisfying 4-term relations and determining
thus a finite type knot invariant. We prove a similar statement for the
transition polynomial of general ribbon graphs and binary delta-matroids
defined by R. Brijder and H. J. Hoogeboom, which defines, as a consequence,
a finite type invariant of links.