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2008 Base-Tangle Decompositions of $n$-String Tangles with $1<n<10$
Mitsuyuki Ochiai, Noriko Morimura
Experiment. Math. 17(1): 1-8 (2008).


This study describes the program bTd, which was developed for the decomposition of any $n$-tangle with $1 < n < 10$} into base {\small$n$}-tangles using the Skein relation. The program enables us to compute HOMFLY polynomials of knots and links with a large number of crossing points within a matter of hours (see Examples 4.4 and 4.5). This contrasts with the results of attempting computations using Hecke algebras $H(q,n)$} with $18 \ge n$. Such a computation did not complete even after a period of thirty days in a recent examination by the first author and F. Kako [Imafuji and Ochiai 02, Murakami 89, Ochiai and Murakami 94, Ochiai and Kako 95]. In this paper, we first introduce two new concepts: an oriented ordered tangle and a subdivision of a tangle. We then present some examples of base-tangle decompositions achieved using the present program along with the corresponding computational times.


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Mitsuyuki Ochiai. Noriko Morimura. "Base-Tangle Decompositions of $n$-String Tangles with $1<n<10$." Experiment. Math. 17 (1) 1 - 8, 2008.


Published: 2008
First available in Project Euclid: 18 November 2008

zbMATH: 1153.57009
MathSciNet: MR2410112

Primary: 57M25 , 57N10

Keywords: knot , mutation , polynomial invariant , tangle decomposition

Rights: Copyright © 2008 A K Peters, Ltd.

Vol.17 • No. 1 • 2008
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