A Note on the Jones Polynomials of 3-Braid Links

Chbili, Nafaa

doi:10.1134/s0037446622050172

Cited by 5 publications

(2 citation statements)

References 23 publications

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“…We conclude then that it cannot be represented as an alternating braid since the closure of an alternating braid is fibered [44]. Similar discussion for the Jones polynomials of 3-braid links can be found in [45].…”

Section: Closed Alternating Braidssupporting

confidence: 71%

The Fox Trapezoidal Conjecture for Alternating Knots

Chbili

2024

Symmetry

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A long-standing conjecture due to R. Fox states that the coefficients of the Alexander polynomial of an alternating knot exhibit a trapezoidal pattern. In other words, these coefficients increase, stabilize, then decrease in a symmetric way. A stronger version of this conjecture states that these coefficients form a log-concave sequence. This conjecture has been recently highlighted by J. Huh as one of the most interesting problems on log-concavity of sequences. In this expository paper, we shall review the various versions of the conjecture, highlight settled cases and outline some future directions.

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