The super-Kauffman conjecture for Turk’s head knots

Let Th(p,q)Th(p,q) denote a Turk’s head knot, with p5p\geq 5 and q4q\geq 4. A knot is super-Kauffman if it admits a minimal alternating diagram whose every crossing has the Kauffman property. Super-Kauffman conjecture. All Turk’s head knots Th(p,q)Th(p,q) with p5p\geq 5 and q4q\geq 4 are super-Kauffman knots. The paper presents this as an open problem, and no resolution is supplied here.

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Primary source

Alessio Di Prisa and Oğuz Şavk, “Turk's head knots and links: a survey”, arXiv:2409.20106 (2026).

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