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Measuring the Length of Petal Projections

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abstract
In this thesis, we explore a new knot invariant which we refer to as the petal length of a knot, denoted \Delta(K), which describes the minimal length among the set of petal projections representing K. In order to define this, we introduce a measurement of the “length” of a cyclic permutation. We prove the monotonicity of this invariant with respect to two of the Reidemeister-type moves devised by Colton et al., and demonstrate an application for identifying when a petal projection corresponds to the unknot. We relate petal length to the ropelength of a knot. In particular, we obtain upper bounds for ropelength in terms of petal length, and conjecture linear bounds for \Delta(K) with respect to the crossing number and ropelength of K.
subject
contributor
Tinlin, Samuel (author)
Parsley, Jason (committee chair)
Mason, Sarah (committee member)
Howards, Hugh (committee member)
date
2022-05-24T08:36:08Z (accessioned)
2022 (issued)
degree
Mathematics and Statistics (discipline)
2023-05-23 (liftdate)
embargo
2023-05-23 (terms)
identifier
http://hdl.handle.net/10339/100756 (uri)
language
en (iso)
publisher
Wake Forest University
title
Measuring the Length of Petal Projections
type
Thesis

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