The Forbidden Number of a Knot

Alissa S. Crans; Blake Mellor; Sandy Ganzell

The Forbidden Number of a Knot

Alissa S. Crans, Blake Mellor, Sandy Ganzell

Mathematics, Statistics and Data Science

Research output: Contribution to journal › Article › peer-review

Abstract

Every classical or virtual knot is equivalent to the unknot via a sequence of extended Reidemeister moves and the so-called forbidden moves. The minimum number of forbidden moves necessary to unknot a given knot is an invariant we call the forbid- den number. We relate the forbidden number to several known invariants, and calculate bounds for some classes of virtual knots.

Original language	English
Pages (from-to)	485-506
Journal	Kyungpook Mathematical Journal
Volume	55
Issue number	2
State	Published - 2015

Keywords

virtual knot
forbidden move
odd writhe

Disciplines

Mathematics

Cite this

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abstract = " Every classical or virtual knot is equivalent to the unknot via a sequence of extended Reidemeister moves and the so-called forbidden moves. The minimum number of forbidden moves necessary to unknot a given knot is an invariant we call the forbid- den number. We relate the forbidden number to several known invariants, and calculate bounds for some classes of virtual knots.",

keywords = "virtual knot, forbidden move, odd writhe",

author = "Crans, {Alissa S.} and Blake Mellor and Sandy Ganzell",

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N2 - Every classical or virtual knot is equivalent to the unknot via a sequence of extended Reidemeister moves and the so-called forbidden moves. The minimum number of forbidden moves necessary to unknot a given knot is an invariant we call the forbid- den number. We relate the forbidden number to several known invariants, and calculate bounds for some classes of virtual knots.

AB - Every classical or virtual knot is equivalent to the unknot via a sequence of extended Reidemeister moves and the so-called forbidden moves. The minimum number of forbidden moves necessary to unknot a given knot is an invariant we call the forbid- den number. We relate the forbidden number to several known invariants, and calculate bounds for some classes of virtual knots.

KW - virtual knot

KW - forbidden move

KW - odd writhe

UR - https://digitalcommons.lmu.edu/math_fac/22

M3 - Article

SN - 0454-8124

VL - 55

SP - 485

EP - 506

JO - Kyungpook Mathematical Journal

JF - Kyungpook Mathematical Journal

IS - 2

ER -

The Forbidden Number of a Knot

Abstract

Keywords

Disciplines

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Cite this