Parity, Skein Polynomials and Categorification
  We investigate an application of crossing parity for the bracket expansion of the Jones polynomial for virtual knots. In addition we consider an application of parity for the arrow polynomial as well as for the categorifications of both polynomials. We present a number of examples found through our calculations. We provide tables of calculations for these invariants on virtual knots with at most 4 real crossings. 
Aaron Kaestner and Louis H. Kauffman
math.GT