On the Harary-Kauffman Conjecture and Turk's Head Knots

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dc.creatorDowdall, Nicholas E.
dc.creatorMattman, Thomas W.
dc.creatorMeek, Kevin
dc.creatorSolis, Pablo R.
dc.date2008-11-01
dc.date.accessioned2026-07-07T10:14:43Z
dc.date.available2026-07-07T10:14:43Z
dc.descriptionThe m,n Turk's Head Knot, THK(m,n), is an "alternating (m,n) torus knot." We prove the Harary-Kauffman conjecture for all THK(m,n) except for the case where m \geq 5 is odd and n \geq 3 is relatively prime to m. We also give evidence in support of the conjecture in that case. Our proof rests on the observation that none of these knots have prime determinant except for THK(m,2) when P_m is a Pell prime.
dc.description16 pages, 12 figures
dc.identifierhttps://arxiv.org/abs/0811.0044
dc.identifierhttp://arxiv.org/abs/0811.0044
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/172975
dc.subjectGeometric Topology
dc.subject57M25
dc.titleOn the Harary-Kauffman Conjecture and Turk's Head Knots
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