Information About

Homfly Polynomial




The name ''HOMFLY'' combines the initials of its co-discoverers: Hoste, Ocneanu, Millett, Freyd, Lickorish, and Yetter. The addition of ''PT'' recognizes independent work carried out by Prztycki and Traczyk.

The polynomial is defined using Skein Relation s:

: P( \mathrm{unknot} ) = 1,\,

: \ell P(L_+) + \ell^{-1}P(L_-) + mP(L_0)=0,\,

where L_+, L_-, L_0 are crossing and smoothing changes on a local region of a link diagram, as indicated in the figure.

  • P(L_2).