AI 中文总结
本文解决了程提出的多元拧数多项式的刻画问题，明确了满足特定条件的整数系数洛朗多项式可作为多虚拟纽结的多元拧数多项式。
AI 中文摘要
程引入了多元拧数多项式，留下了关于该不变量刻画的问题。本文通过证明：具有整数系数的洛朗多项式$f$可实现为某个多虚拟纽结的多元拧数多项式，当且仅当$f(1,\boldsymbol{\text{…}},1)=0$且$\frac{d}{dt}f(t,\boldsymbol{\text{…}},t)\bigg|_{t=1}=0$，解决了该问题。
英文摘要
Cheng introduces the multivariate writhe polynomial, leaving a question regarding the characterization of this invariant. In this paper, we resolve this question by proving that a Laurent polynomial $f$ with integer coefficients can be realized as the multivariate writhe polynomial of some multi-virtual knot if and only if $f(1,\dots,1)=0$ and $\left. \frac{d}{dt} f(t, \dots, t) \right\vert{}_{t=1} = 0$.
Comments5 pages, 6 figures
