Publication Year

2002

Keywords

Mathematics, stick numbers, knot theory, groups

Disciplines

Applied Mathematics | Mathematics

Abstract

A portion of knot theory is devoted to determining the minimum number of sticks required to construct a know. For knots with eleven crossings or fewer, there are no known constructions with fewer sticks than crossings. However, this research has produced constructions of two twelve crossing knots with eleven sticks. Given that there are no nine-crossing prime knots that can be constructed with eight sticks, the smallest crossing number for any prime knot that can be constructed with fewer sticks than crossings is between ten and twelve crossings (inclusive). The method of construction used in this research, namely clasping, has produced infinite families of knots with fewer sticks than crossings. Moreover, groups have emerged within the set of tools that we developed to produce knots with fewer crossings.

Note: A portion of Research Funded by NSF-REU Grant DMS-9987955, and Cal State San Bernardino, San Bernardino CA 92407.

Department 1 Awarding Honors Status

Mathematics

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