Uniform folded ribbonlength conjecture for pretzel links

Let LL be a three-strand pretzel link P(p,q,r)P(p,q,r), with folded ribbon realization LwL_w, and let Rib(Lw){\operatorname{Rib}}(L_w) denote its folded ribbonlength. Pretzel-link uniformity conjecture. There is a constant C>0C>0 such that, for all (p,q,r)(p,q,r) pretzel links,

Rib(Lw)C.{\operatorname{Rib}}(L_w)\leq C.

The conjecture asserts a uniform bound independent of the three twist parameters; the paper motivates it by noting that arbitrarily many half-twists can be constructed with finite folded ribbonlength and that the strands can be joined with a finite additional amount.

Sources & referencesView supporting material

Primary source

Zhicheng Chen, Elizabeth Denne, Kyle Patterson and Timi Patterson, “Ribbonlength upper bounds for small crossing knots and links”, arXiv:2510.16190 (2025).

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