A knot [Formula: see text] is a parent of a knot [Formula: see text] if there exists a minimal crossing diagram [Formula: see text] of [Formula: see text] such that a subset of the crossings of [Formula: see text] can be changed to produce a diagram of [Formula: see text]. A knot [Formula: see text] with crossing number [Formula: see text] is fertile if for any prime knot [Formula: see text] with crossing number less than [Formula: see text], [Formula: see text] is a parent of [Formula: see text]. It is known that only [Formula: see text] are fertile for knots up to 10 crossings. However it is unknown whether there exist other fertile knots. A knot shadow is a diagram without over/under information at all crossings. In this paper, we introduce a definition of fertility for knot shadows. We show that if an alternating knot [Formula: see text] is fertile then the crossing number of [Formula: see text] is less than eight.

中文翻译：

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关于结影的生育力

如果存在 [公式：见文本] 的最小交叉图 [公式：见文本]，则结 [公式：见文本] 是结 [公式：见文本] 的父节点，使得 [公式：见文本] 的交叉子集:see text] 可以更改为 [Formula: see text] 的图表。如果任何素数结 [公式：见正文] 的交叉数小于 [公式：见正文]，则 [公式：见正文] 的结 [公式：见正文] 是可生育的[公式：见正文]的父级。众所周知，只有 [公式：见正文] 可产生多达 10 个交叉点。但尚不清楚是否存在其他肥沃结。结阴影是在所有交叉口都没有过度/不足信息的图表。在本文中，我们介绍了节点阴影的生育力定义。我们证明，如果一个交替的结[公式：