We introduce the notion of N-reduced dynamical cocycles and use these objects to define enhancements of the rack counting invariant for classical and virtual knots and links. We provide examples to show that the new invariants are not determined by the rack counting invariant, the Jones polynomial or the generalized Alexander polynomial.
Crans, A.; Nelson, S.; and Sarkar, A. “Enhancements of the rack counting invariant via N-reduced dynamical cocycles.” New York Journal of Mathematics, Vol. 18 (2012): 337 – 351.