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The program "LinKnot"-its theoretical background and experimental mathematics results obtained
by
Slavik Jablan
The Mathematical Institute, Knez Mihailova 35, P.O.Box 367, 11001 Belgrade, Serbia&Montenegro
Coauthors: Radmila Sazdanovic
The program "LinKnot" can be very efficiently used in experimental mathematics, as a tool for computing data (knot and link invariants, polynomials, signature, unknotting and unlinking numbers, etc.) for very large families of knots and links (KLs). From them, new conjectures can be made.
We will present the results connected to Bernhard-Jablan Conjecture on unknotting and unlinking numbers, projection gap, amphichirality, and Alexander polynomials derived in general form for diffrerent families of KLs. For example, a projection gap in rational KLs occurs for the first time for the link 414 with n=9 crossings. For n=10 the only case is the famous knot 514; for n=11 we have the knot 4142, and the links 434, 614, 4142, 5132, 51113 with the same property; for n=12 there are five such knots: 714, 534, 4143, 6132, 61113; for n=13 there are 7 knots 4414, 6142, 41314, 51322, 231412, 511132, 513112 and 16 links 616, 634,814, 5152, 5332, 6133, 7132, 34132, 41422, 51115, 61123, 71113, 241312, 411142, 611122 and 4211113. All thet results can be extended to infinite families of KLs.
Date received: November 10, 2003
Copyright © 2003 by the author(s). The author(s) of this work and the organizers of the conference have granted their consent to include this abstract in Topology Atlas. Document # camw-03.