An extension of Stanley's chromatic symmetric function to binary delta-matroids

Stanley's symmetrized chromatic polynomial is a generalization of the ordinary to graph invariant with values in ring polynomials infinitely many variables. The specialization one. To each orientable embedded single vertex, simple associated, which called intersection graph. As result, we can define for any vertex. Our goal extend graphs arbitrary number vertices, and not necessarily orientable. In contrast well-known extensions of, say, Tutte from abstract [4], our extension based on structure underlying additional information about embedding. Instead, consider binary delta-matroid associated an extended Stanley as delta-matroids. We show that, similarly graphs, satisfies 4-term relations that introduce delta-matroids [7]. For function produces knot by means correspondence between knots. Analogously may interpret suggested links, using links.