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- Publisher
- Wiley
- Copyright
- © London Mathematical Society
- ISSN
- 0024-6093
- eISSN
- 1469-2120
- DOI
- 10.1112/blms/14.5.397
- Publisher site
- See Article on Publisher Site
Abstract
C . KEARTON A well-known result of H . Schubert [6] states that every classical kno t S'cS factorises uniquely into prime knots. It is also known that unique factorisation fails n n + 2 for n-knots (S <= S ) when n > 3; (see [1, 2, 3, 4]). In this note we give an example of a 3-knot which not only factorises into irreducibles in two different ways, but has a different number of factors in each case. Consider the following matrices, taken from [1, p. 589] and [2, p. 502]. 0 0 0 0 - 1 - 2 - 2 - 1 - 1 0 0 0 0 0 - 2 - 2 0 0 0 0 0 0 - 1 - 2 1 0 0 0 0 0 0 - 1 A = 2 1 0 0 0 0 0 0 2 2 1 0 0 0 0 0 1 2 2 1 0 0 0 0 0 1 2 2 1 0 0 0 1 - 1 - 2 - 3 - 3 - 2 - 1 - 3 1 - 1 2 - 2 - 3 - 3 - 3 - 2 _
Journal
Bulletin of the London Mathematical Society – Wiley
Published: Sep 1, 1982