Mp-small summands increase knot width.
Hendricks, Jacob (2004)
Algebraic & Geometric Topology
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Hendricks, Jacob (2004)
Algebraic & Geometric Topology
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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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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.
Yasutaka Nakanishi (1996)
Revista Matemática de la Universidad Complutense de Madrid
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This note is a continuation of a former paper, where we have discussed the unknotting number of knots with respect to knot diagrams. We will show that for every minimum-crossing knot-diagram among all unknotting-number-one two-bridge knot there exist crossings whose exchange yields the trivial knot, if the third Tait conjecture is true.
S. Jablan, R. Sazdanovic (2003)
Visual Mathematics
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Willerton, Simon (2002)
Experimental Mathematics
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Skip Pennock (2005)
Visual Mathematics
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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.
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.