On Fox's trapezoidal conjecture for closed 3-braids

Marwa E. Alrefai, Nafaa Chbili

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

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 languageEnglish
Article number2150002
JournalInternational Journal of Mathematics
Volume32
Issue number1
DOIs
Publication statusPublished - Jan 2021

Keywords

  • 3-braids
  • Alexander polynomial
  • Alternating links
  • trapezoidal conjecture

ASJC Scopus subject areas

  • Mathematics(all)

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