P-polynomial

A 2-variable oriented knot polynomial P_L(a, z) motivated by the Jones polynomial . Its name is an acronym for the last names of its co-discoverers: Hoste, Ocneanu, Millett, Freyd, Lickorish, and Yetter . Independent work related to the HOMFLY polynomial was also carried out by Prztycki and Traczyk. HOMFLY polynomial is defined by the skein relationship a^(-1) P_(L_+)(a, z) - a P_(L_-)(a, z) = z P_(L_0)(a, z) (Doll and Hoste 1991), where v is sometimes written instead of a or, with a slightly different relationship, as α P_(L_+)(α, z) - α^(-1) P_(L_-)(α, z) = z P_(L_0)(α, z) (Kauffman 1991).

Alexander polynomial | Jones polynomial | knot polynomial