A bound for orderings of Reidemeister moves

Gold, Julian

doi:10.2140/agt.2013.13.3099

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2022

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“…In this paper, we discuss such a simple sequence. There are some related papers in this topic (see [1], [2] [3], [4], [5], [7]).…”

Section: Introductionmentioning

confidence: 99%

Ordering sequence for link diagrams with respect to Ridemeister moves I and III

Sasaki¹

2022

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We prove that there exist infinitely many pairs of RI-III related (see Definition 2.1 in this paper) trivial knot diagrams that are not transformed into each other by a sequence of Reidemeister moves I, followed by a sequence of Reidemeister moves III, followed by a sequence of Reidemeister moves I. To create a simple sequence for RI-III related link diagrams instead of the ordinary ordering sequence, we prove that RI-III related link diagrams are always transformed into each other by applying an Igeneralized ordering sequence.

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“…In this paper, we discuss such a simple sequence. There are some related papers in this topic (see [1], [2] [3], [4], [5], [7]).…”

Section: Introductionmentioning

confidence: 99%