13 problems

Let $L$ be a knot or link type, let ${\operatorname{Cr}}(L)$ denote its crossing number, and let ${\operatorname{Rib}}([L])$ denote the infimal folded ribbonlength of the knot or l…

Let $L$ be a link, let $c(L)$ denote its crossing number, and let $\mathrm{Rib}(L)$ denote its folded ribbonlength, defined as the infimum of the core length divided by the ribbon…

Let $K$ be a knot or link, let $c(K)$ denote its crossing number, and let $\mathrm{Rib}(K)$ denote its ribbonlength. For constants $c_1,c_2>0$ and exponents $\alpha,\beta$, Diao–Ku…

Let $T(2,q)$ denote a $(2,q)$-torus link, let $[T(2,q)]$ denote its link type, and let ${\operatorname{Rib}}([T(2,q)])$ denote its infimal folded ribbonlength. Uniform torus-link c…

Let $K_{8,3}$ be the $(8,3)$ torus knot, which the paper describes as forming an eight-sided regular polygon without a central gap. Its Ribbonlength is the minimum length-to-width…

Let $q$ be a positive integer and let $K_{q+1,q}$ denote the $(q+1,q)$ torus knot. The closed Ribbonlength is the minimum length-to-width ratio among closed ribbon presentations. T…

Let $K_{4,3}$ be the $(4,3)$ torus knot, and let Ribbonlength mean the minimum length-to-width ratio among ribbon presentations of a knot. The construction in the paper has ratio…

Let $q$ be a positive integer and let $K_{q+1,q}$ denote the $(q+1,q)$ torus knot. Its closed Ribbonlength conjecture is … The conjecture concerns the minimum length-to-width ratio…

Let $L$ be a three-strand pretzel link $P(p,q,r)$, with folded ribbon realization $L_w$, and let ${\operatorname{Rib}}(L_w)$ denote its folded ribbonlength. Pretzel-link uniformity…

Let $T(2,3)$ be the trefoil knot, and consider folded ribbon realizations whose ribbon is a topological Möbius band. Let ${\operatorname{Rib}}$ denote folded ribbonlength and take…

Let $K$ be a folded ribbon trefoil knot that is topologically a Möbius band, and let $\operatorname{Rib}([K]_{\mathrm{Möb}})$ denote its infimal folded ribbonlength in the Möbius-b…

Let $K$ be a folded ribbon trefoil knot, and let $\operatorname{Rib}([K])$ denote the infimal folded ribbonlength over its diagram-equivalence class. Trefoil folded ribbonlength co…

Evidence for the ribbonlength exponent conjecture. For each $p$ in this range, there is a constant $c_p>0$ such that