Geodesic
GAPS BETWEEN CONSECUTIVE UNTWISTING NUMBERS
Glasgow mathematical journal, Tome 63 (2021) no. 1, pp. 59-65

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DOI

For p ≥ 1, one can define a generalisation of the unknotting number tup called the pth untwisting number, which counts the number of null-homologous twists on at most 2p strands required to convert the knot to the unknot. We show that for any p ≥ 2 the difference between the consecutive untwisting numbers tup–1 and tup can be arbitrarily large. We also show that torus knots exhibit arbitrarily large gaps between tu1 and tu2. 
MCCOY, DUNCAN. GAPS BETWEEN CONSECUTIVE UNTWISTING NUMBERS. Glasgow mathematical journal, Tome 63 (2021) no. 1, pp. 59-65. doi: 10.1017/S0017089520000014
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     title = {GAPS {BETWEEN} {CONSECUTIVE} {UNTWISTING} {NUMBERS}},
     journal = {Glasgow mathematical journal},
     pages = {59--65},
     year = {2021},
     volume = {63},
     number = {1},
     doi = {10.1017/S0017089520000014},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089520000014/}
}
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