标题： 考夫曼约束系数 Kw 显示英文标题

标题： The Kauffman Constraint Coefficients Kw

摘要： Kauffman约束系数Kw及其对应的元素Ew被呈现为构造Kauffman的Theta函数的(beta)导数的解。 此外，提供了一个新的递归关系来构造Theta的(beta)导数，该关系仅需要操作替换和求和；这在算法上简化了Kauffman的原始技术。 为了演示Kw，我们从对应的Elementals Ew生成Theta的(9)导数的30个Kw系数，并发现我们的结果与Kauffman的Mathematica\texttrademark 解决方案完全一致。 我们进一步给出了Theta的(12)导数的两个系数的计算，并邀请读者使用Mathematica\texttrademark 或其他任何方法来计算和验证我们的结果。 最后，我们给出了Theta的(40)导数的一个系数的具有挑战性的计算；由于涉及的排列数量巨大，Mathematica\texttrademark 方法可能需要大量的计算机资源才能在合理的时间内获得解决方案。 显示英文摘要

摘要： The Kauffman Constraint Coefficients Kw and their corresponding Elementals Ew are presented as solutions to the construction of the (beta)-derivative of Kauffman's Theta-function. Additionally, a new recursion relation is provided to construct the (beta)-derivative of Theta that requires only operational substitutions and summations; this algorithmically simplifies Kauffman's original technique. To demonstrate Kw, we generate the 30 Kw Coefficients from the corresponding Elementals Ew for the (9)-derivative of Theta and find that our results are in complete agreement with Kauffman's Mathematica\texttrademark solutions. We further present a calculation of two coefficients for the (12)-derivative of Theta and invite readers to use Mathematica\texttrademark or any other means to calculate and verify our results. Finally, we present a challenging calculation for a coefficient of the (40)-derivative of Theta; owing to the vast numbers of permutations involved, a Mathematica\texttrademark approach may require substantial computer resources to obtain the solution in a reasonable time.