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A polynomial upper bound on Reidemeister moves, preprint (arXiv : 1302.0180 [math.GT
, 2013
"... We prove that any diagram of the unknot with c crossings may be reduced to the trivial diagram using at most (236 c)11 Reidemeister moves. 1. ..."
Abstract

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We prove that any diagram of the unknot with c crossings may be reduced to the trivial diagram using at most (236 c)11 Reidemeister moves. 1.