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The almost alternating diagrams of the trivial knot
Author(s) -
Tsukamoto Tatsuya
Publication year - 2009
Publication title -
journal of topology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.447
H-Index - 31
eISSN - 1753-8424
pISSN - 1753-8416
DOI - 10.1112/jtopol/jtp001
Subject(s) - knot (papermaking) , mathematics , combinatorics , composite material , materials science
Bankwitz characterized the alternating diagrams of the trivial knot. A non‐alternating diagram is called almost alternating if one crossing change makes the diagram alternating. We characterize the almost alternating diagrams of the trivial knot. As a corollary, we determine the unknotting number one alternating knots with the property that the unknotting operation can be done on its alternating diagram.