Abstract
An old and challenging conjecture proposed by Fox in 1962 states that the coefficients of the Alexander polynomial of any alternating knot are trapezoidal. In other words, these coefficients, increase, stabilize then decrease in a symmetrical way. This curious behavior of the Alexander polynomial has been confirmed in several special cases of alternating knots. The purpose of this paper is to prove that the conjecture holds for some families of alternating knots of braid index 3.
Original language | English |
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Article number | 2150002 |
Journal | International Journal of Mathematics |
Volume | 32 |
Issue number | 1 |
DOIs | |
Publication status | Published - Jan 2021 |
Keywords
- 3-braids
- Alexander polynomial
- Alternating links
- trapezoidal conjecture
ASJC Scopus subject areas
- General Mathematics