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Supercoiled tangles and stick numbers of 2-Bridge links

Erik Insko

Department of Mathematics, Florida Gulf Coast University, Fort Myers, FL 33965, USA

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and

Rolland Trapp

Department of Mathematics, California State University, 5500 University Pkwy, San Bernardino, CA 92407, USA

Corresponding author.

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https://doi.org/10.1142/S0218216515500297Cited by:0 (Source: Crossref)

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 . We also show that if c > 12n + 3, then minimal stick representatives do not admit minimal crossing projections.

Keywords:

AMSC: 57M25, 57M27

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