A braid index is the least number of strings needed to make a closed braid representation of a link. The braid index is equal to the least number of Seifert circles in any projection of a knot. Also, for a nonsplittable link with link crossing number c(L) and braid index i(L), c(L)>=2[i(L) - 1] (Ohyama 1993). Let E be the largest and e the smallest power of ℓ in the HOMFLY polynomial of an oriented link, and i be the braid index.

braid | braid group | braid word | knot | link