Chbili–Qazaqzeh Jones-coefficient conjecture for quasi-alternating links

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Let LL be a link whose Jones polynomial is written as

VL(t)=∑i=0maiti,V_L(t)=\displaystyle\sum_{i=0}^{m}a_i t^i,

where m≥0m\geq 0, a0≠0a_0\neq 0, and am≠0a_m\neq 0. Chbili–Qazaqzeh conjecture. If LL is a prime quasi-alternating link, other than a (2,n)(2,n)-torus link, then

aiai+1<0for all 0≤i≤m−1.a_i a_{i+1}<0\qquad\text{for all }0\leq i\leq m-1.

The conjecture concerns strict sign alternation of consecutive Jones-polynomial coefficients for prime quasi-alternating links, excluding (2,n)(2,n)-torus links. No resolution is given in the supplied context.

References

Primary source

Hamid Abchir and Mohammed Sabak, “Generating links that are both quasi-alternating and almost alternating”, arXiv:2003.13725 (2020).

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