Eskimo bowline structure of the knot was not identified by Clifford Ashley (in 1944). All of the maneuvers to tie this knot are generally in the opposite (or 'anti' direction) relative to the bowline. Dan Lehman regards the general, bowline-like structure as an 'anti-bowline' in the sense of "anti-clockwise": in that with regard to the main nipping loop, the tail on returning from forming the eye is brought through this loop in the opposite direction relative to what is done for a bowline. When this knot is ring-loaded – and the knot effectively becomes an end-to-end knot – it is effectively a
Arf invariant of a knot graph associated to a knot diagram. This approach to the Arf invariant is by Raymond Robertello. Let be the Alexander polynomial of the knot. Then the Arf invariant is the residue of modulo 2, where "r" = 0 for "n" odd, and "r" = 1 for "n" even. Kunio Murasugi proved that the Arf invariant is zero if and only if Δ(−1) formula_8 ±1 modulo 8. From the Fox-Milnor criterion, which tells us that the Alexander polynomial of a slice knot formula_9 factors as formula_10 for some polynomial formula_11 with integer coefficients, we know that the determinant formula_12 of a