Open AccessThe Forbidden Number of a Knot
Author(s) -
Alissa S. Crans,
Blake Mellor,
Sandy Ganzell
Publication year - 2015
Publication title -
kyungpook mathematical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.287
H-Index - 19
eISSN - 1225-6951
pISSN - 0454-8124
DOI - 10.5666/kmj.2015.55.2.485
Subject(s) - unknot , mathematics , knot (papermaking) , tricolorability , knot invariant , knot theory , combinatorics , chemical engineering , engineering
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.
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