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- Title
SIMPLIFIED NUMERICAL FORM OF UNIVERSAL FINITE TYPE INVARIANT OF GAUSS WORDS.
- Authors
FUKUNAGA, TOMONORI; YAMAGUCHI, TAKAYUKI; YAMANOI, TAKAAKI
- Abstract
In this paper, we study the finite type invariants of Gauss words. In the Polyak algebra techniques, we reduce the determination of the group structure to transformation of a matrix into its Smith normal form and we give the simplified form of a universal finite type invariant by means of the isomorphism of this transformation. The advantage of this process is that we can implement it as a computer program. We obtain the universal finite type invariant of degrees 4, 5 and 6 explicitly. Moreover, as an application, we give the complete classification of Gauss words of rank 4 and the partial classification of Gauss words of rank 5 where the distinction of only one pair remains.
- Subjects
INVARIANTS (Mathematics); GAUSSIAN function; HYPERGEOMETRIC series; NUMERICAL analysis; FINITE groups; ISOMORPHISM (Mathematics)
- Publication
Journal of Knot Theory & Its Ramifications, 2013, Vol 22, Issue 8, p-1
- ISSN
0218-2165
- Publication type
Article
- DOI
10.1142/S0218216513500375