We conjecture a closed-form expression of HOMFLY-PT invariants of double twist knots colored by rectangular Young diagrams where the twist is encoded in interpolation Macdonald polynomials. We also put forth a conjecture of cyclotomic expansions of HOMFLY-PT polynomials colored by rectangular Young diagrams for any knot.

中文翻译：

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矩形杨氏图着色的 HOMFLY-PT 的循环扩展

我们推测了由矩形杨氏图着色的双扭曲结的 HOMFLY-PT 不变量的闭式表达式，其中扭曲在插值 Macdonald 多项式中编码。我们还提出了对任何结的矩形杨图着色的 HOMFLY-PT 多项式的分圆展开的猜想。