Research ArticleNo Access

Ribbonlength and crossing number for folded ribbon knots

Department of Mathematics, Washington & Lee University, Lexington, VA 24450, USA

https://doi.org/10.1142/S0218216521500280Cited by:3 (Source: Crossref)

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 $c_{1} Cr {(K)}^{2}$ , and also by $c_{2} Cr {(K)}^{3 / 2}$ . 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 $Cr (K) \leq$ 12,748.

Keywords:

AMSC: 57K10

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