Cowboy bowline so easily pushed back by accident. However, there is no documentation to confirm this claim, and some Dutch knot tyers outright deny it. Another piece of unverified lore is that it is called a winter bowline because the exposed working end on the outside would blow in the wind and prevent it from freezing to the loop on ships in the north Atlantic during winter. (This suggests that the standard bowline would be the summer bowline.) "The Ashley Book of Knots" states that it is "distinctly inferior" to the standard bowline because of its similarity to the left-hand sheet bend.
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