论文标题
克里斯托佛尔的言语和强大的福克斯猜想是两桥结
Christoffel words and the strong Fox conjecture for two-bridge knots
论文作者
论文摘要
梯形狐狸的猜想指出，交替结的亚历山大多项式的系数序列是单峰的。我们的动机是一个更难的问题，即强烈的福克斯猜想，该猜想询问交替结的亚历山大多项式的系数序列是否实际上是对数 - concave。我们的方法是引入与ChristOffel单词相关的多项式$δ（t）$，并证明其系数序列是对数concave。这意味着对两桥结的强烈福克斯猜想。
The trapezoidal Fox conjecture states that the coefficient sequence of the Alexander polynomial of an alternating knot is unimodal. We are motivated by a harder question, the strong Fox conjecture, which asks whether the coefficient sequence of the Alexander polynomial of alternating knots is actually log-concave. Our approach is to introduce a polynomial $Δ(t)$ associated to a Christoffel word and to prove that its coefficient sequence is log-concave. This implies the strong Fox conjecture for two-bridge knots.
