Supercoiled Tangles and Stick Numbers of 2-bridge Links

Erik Insko; Rolland Trapp

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arXiv · 1308.0709

Supercoiled Tangles and Stick Numbers of 2-bridge Links

Erik Insko·Rolland Trapp

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Abstract

Utilizing both twisting and writhing, we construct integral tangles with few sticks, leading to an efficient method for constructing polygonal 2-bridge links. Let L be a two bridge link with crossing number c, stick number s, and n tangles. It is shown that s is less than or equal to 2/3 c + 2n+3 . We also show that if c > 12n+3, then minimal stick representatives do not admit minimal crossing projections.

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Erik Insko, Rolland Trapp. 2013-08-03. Supercoiled Tangles and Stick Numbers of 2-bridge Links. https://arxiv.org/abs/1308.0709

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