论文标题
与广义康威对话 - 戈登类型的一致性
Converses to generalized Conway--Gordon type congruences
论文作者
论文摘要
众所周知，对于$ n \ ge 7 $顶点上的每个空间完整图，在汉密尔顿结上的第二个系数的总和是$ r_ {n} $ modulo $（n-5）！ $ n \ neq 8k，8k+7 $。尤其是$ n = 7 $的情况以conway闻名 - 戈登$ k_ {7} $定理。相反，在本文中，我们证明了每个整数$（N-5）！ q + r_ {n} $被实现为在$ n $顶点上的一些空间完整图中，在汉密尔顿结上的第二个系数的汇总。
It is known that for every spatial complete graph on $n\ge 7$ vertices, the summation of the second coefficients of the Conway polynomials over the Hamiltonian knots is congruent to $r_{n}$ modulo $(n-5)!$, where $r_{n} = (n-5)!/2$ if $n=8k,8k+7$, and $0$ if $n\neq 8k,8k+7$. In particular the case of $n=7$ is famous as the Conway--Gordon $K_{7}$ theorem. In this paper, conversely, we show that every integer $(n-5)! q + r_{n}$ is realized as the summation of the second coefficients of the Conway polynomials over the Hamiltonian knots in some spatial complete graph on $n$ vertices.
