Turk's head

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Noun1.Turk's head - an ornamental knot that resembles a small turbanTurk's head - an ornamental knot that resembles a small turban
knot - any of various fastenings formed by looping and tying a rope (or cord) upon itself or to another rope or to another object
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For each n [member of] [Z.sup.+], the Turk's head knot on 3 strands, denoted THK(3, n), is the closure of the braid [([[sigma].sub.2] [[sigma].sub.1.sup.-1]).sup.n] [member of] [B.sub.3].
Bearing in mind that if gcd(r, [u.sub.n-1]) > 1, there is a non-trivial r-coloring of THK(3, n) (Corollary 1.2), then, provided r is prime, [psi](r) yields the least number of [[sigma].sub.2] [[sigma].sub.1.sup.-1]'s we have to juxtapose in order to obtain a non-trivial r-coloring for a Turk's head knot on three strands, namely THK(3, [psi](r)).
Bearing in mind that if gcd(r, [u.sub.n-1]) > 1, there is a non-trivial r-coloring of THK(3, n) (Corollary 1.2), then, provided r is prime, [psi](r) yields the least number of [[sigma].sub.2][[sigma].sup.-1.sub.1]'s we have to juxtapose in order to obtain a non-trivial r-coloring for a Turk's head knot on three strands, namely THK(3, [psi](r)).