Can computers discover ideal knots?
Rawdon, Eric J. (2003)
Experimental Mathematics
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Rawdon, Eric J. (2003)
Experimental Mathematics
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Vaughan Jones, Józef Przytycki (1998)
Banach Center Publications
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We show that Lissajous knots are equivalent to billiard knots in a cube. We consider also knots in general 3-dimensional billiard tables. We analyse symmetry of knots in billiard tables and show in particular that the Alexander polynomial of a Lissajous knot is a square modulo 2.
Monica Meissen (1998)
Banach Center Publications
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The minimal number of edges required to form a knot or link of type K is the edge number of K, and is denoted e(K). When knots are drawn with edges, they are appropriately called piecewise-linear or PL knots. This paper presents some edge number results for PL knots. Included are illustrations of and integer coordinates for the vertices of several prime PL knots.
Richard Randell (1998)
Banach Center Publications
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We study numerical and polynomial invariants of piecewise-linear knots, with the goal of better understanding the space of all knots and links. For knots with small numbers of edges we are able to find limits on polynomial or Vassiliev invariants sufficient to determine an exact list of realizable knots. We thus obtain the minimal edge number for all knots with six or fewer crossings. For example, the only knot requiring exactly seven edges is the figure-8 knot.
Isabel Darcy, De Sumners (1998)
Banach Center Publications
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The following is an expository article meant to give a simplified introduction to applications of topology to DNA.
Ekholm, Tobias, Wolff, Maxime (2002)
Algebraic & Geometric Topology
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Peter Cromwell (1998)
Banach Center Publications
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s paper presents some examples and a survey of results concerning a new way of presenting knots and links, together with the corresponding link invariant. More detailed accounts are given in [Cr, C-N, Nu1, Nu2, Nu3].
Schmitt, Peter (1997)
Beiträge zur Algebra und Geometrie
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Dugopolski, Mark J. (1985)
International Journal of Mathematics and Mathematical Sciences
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Willerton, Simon (2002)
Experimental Mathematics
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P. V. Koseleff, D. Pecker (2014)
Banach Center Publications
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We show that every knot can be realized as a billiard trajectory in a convex prism. This proves a conjecture of Jones and Przytycki.
Ljiljana Radović, Slavik Jablan (2013)
Publications de l'Institut Mathématique
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