Geodesic
On a problem in effective knot theory
Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 9 (1998) no. 4, pp. 299-306 Cet article a éte moissonné depuis la source Biblioteca Digitale Italiana di Matematica

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The following problem is investigated: «Find an elementary function \( F (n) : \mathbf{ Z }\rightarrow \mathbf{ Z} \) such that if \( \Gamma \) is a knot diagram with \( n \) crossings and the corresponding knot is trivial, then there is a sequence of Reidemeister moves that proves triviality such that at each step we have less than \( F (n) \) crossings». The problem is shown to be equivalent to a problem posed by D. Welsh in [7] and solved by geometrical techniques (normal surfaces). 
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     author = {Galatolo, Stefano},
     title = {On a problem in effective knot theory},
     journal = {Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni},
     pages = {299--306},
     year = {1998},
     volume = {Ser. 9, 9},
     number = {4},
     zbl = {1001.57007},
     mrnumber = {MR1722788},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/RLIN_1998_9_9_4_a5/}
}
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Galatolo, Stefano. On a problem in effective knot theory. Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 9 (1998) no. 4, pp. 299-306. http://geodesic.mathdoc.fr/item/RLIN_1998_9_9_4_a5/