Folded ribbonlength of 2-bridge knots
| Autor: | Hyoungjun Kim, Sungjong No, Hyungkee Yoo |
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| Rok vydání: | 2022 |
| Předmět: | |
| DOI: | 10.48550/arxiv.2208.03669 |
| Popis: | A ribbon is a two-dimensional object with one-dimensional properties which is related with geometry, robotics and molecular biology. A folded ribbon structure provides a complex structure through a series of folds. We focus on a folded ribbon with knotted core. The folded ribbonlength $Rib(K)$ of a knot $K$ is the infimum of the quotient of length by width among the ribbons representing a knot type of $K$. This quantity tells how efficiently the folded ribbon is realized. Kusner conjectured that folded ribbonlength is bounded by a linear function of the minimal crossing number $c(K)$. In this paper, we confirm that the folded ribbonlength of a 2-bridge knot $K$ is bounded above by $2c(K)+2$. Comment: 9 pages, 7 figures |
| Databáze: | OpenAIRE |
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