Ribbonlength and crossing number for folded ribbon knots

Abstract

We study Kauffman's model of folded ribbon knots: knots made of a thin strip of paper folded flat in the plane. The ribbonlength is the length to width ratio of such a folded ribbon knot. We show for any knot or link type that there exist constants $c_1,c_2>0$ such that the ribbonlength is bounded above by $c_1\cdot Cr(K{)}^2$, and also by $c_2\cdot Cr(K{)}^{3/2}$. We use a different method for each bound. The constant $c_1$ is quite small in comparison to $c_2$, and the first bound is lower than the second for knots and links with $Cr(K)\le$ 12,748.

19 pages, 7 figures. Revision 1: Correction to Theorem 2

References in corpus (1)

• Ribbonlength of families of folded ribbon knots

Cited by in corpus (2)

• Ribbonlength of families of folded ribbon knots
• Linking number and folded ribbon unknots