Chbili–Qazaqzeh's Jones polynomial conjecture for quasi-alternating links

Let LL be a prime quasi-alternating link that is not a (2,n)(2,n)-torus link, and write its Jones polynomial as

VL(t)=i=nmciti.V_L(t)=\sum_{i=n}^{m}c_i t^i.

Chbili–Qazaqzeh's conjecture. The coefficients satisfy

cici+1<0c_i c_{i+1}<0

for all nim1n\leq i\leq m-1.

The conjecture extends the known alternating-coefficient property of prime alternating links to prime quasi-alternating links. The source states that it was subsequently proved that, if a quasi-alternating link satisfies this conjecture, then any link obtained from it by the Champernowne–Kofman twisting construction also satisfies it.

Sources & referencesView supporting material

Primary source

Nafaa Chbili and Kirandeep Kaur, “Extending Quasi-Alternating Links”, arXiv:2007.07770 (2020).

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