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math.GT2021
Hard Diagrams of the Unknot
Benjamin A. Burton, Hsien-Chih Chang, Maarten Löffler +5
We present three "hard" diagrams of the unknot. They require (at least) three extra crossings before they can be simplified to the trivial unknot diagram via Reidemeister moves in…
math.GT2020★ 1 cited
Tightening Curves on Surfaces Monotonically with Applications
Hsien-Chih Chang, Arnaud de Mesmay
We prove the first polynomial bound on the number of monotonic homotopy moves required to tighten a collection of closed curves on any compact orientable surface, where the number…