论文标题
普遍的鱼潮的数字和圆环结
Generalized Fishburn numbers and torus knots
论文作者
论文摘要
安德鲁斯和卖家最近启动了Fishburn数字的算术特性的研究。在本文中，我们证明了Prime Power的一致性。这些数字是Kontsevich-Zagier系列$ \ Mathscr {f} _ {t}（q）$的$ 1-Q $扩展系数的系数。证明使用了Ahlgren，Kim和Lovejoy的强大可分裂性结果，以及用于$ \ Mathscr {f} _ {t}（q）$的新的“奇怪身份”。
Andrews and Sellers recently initiated the study of arithmetic properties of Fishburn numbers. In this paper, we prove prime power congruences for generalized Fishburn numbers. These numbers are the coefficients in the $1-q$ expansion of the Kontsevich-Zagier series $\mathscr{F}_{t}(q)$ for the torus knots $T(3,2^t)$, $t \geq 2$. The proof uses a strong divisibility result of Ahlgren, Kim and Lovejoy and a new "strange identity" for $\mathscr{F}_{t}(q)$.
