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The complexity of lattice knots

✍ Scribed by Y. Diao; C. Ernst

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
429 KB
Volume
90
Category
Article
ISSN
0166-8641

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✦ Synopsis

A family of polygonal knots K, on the cubical lattice is constructed with the property that the quotient of length L(Kn) over the crossing number Cr(Kn) approaches zero as L approaches infinity. More precisely Cr(K,) = 0(L(Kn)4/3).

It is shown that this construction is optimal in the sense that for any knot K on the cubical lattice with length L and Cr crossings Cr < 3.2L413.

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