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تسجيل مستخدم جديدHard Diagrams of the Unknot
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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 $mathbb{S}^2$. Both examples are constructed by applying previously proposed methods. The proof of their hardness uses significant computational resources. We also determine that no small standard example of a hard unknot diagram requires more than one extra crossing for Reidemeister moves in $mathbb{S}^2$.
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