Ito–Takimura recently defined a splice-unknotting number [Formula: see text] for knot diagrams. They proved that this number provides an upper bound for the crosscap number of any prime knot, asking whether equality holds in the alternating case. We answer their question in the affirmative. (Ito has independently proven the same result.) As an application, we compute the crosscap numbers of all prime alternating knots through at least 13 crossings, using Gauss codes.

中文翻译：

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通过不打结拼接的交替结的 Crosscap 数量

Ito–Takimura 最近为结图定义了一个拼接解开数 [公式：见正文]。他们证明了这个数字为任何素数结的交叉帽数提供了一个上限，询问在交替情况下是否相等。我们肯定地回答他们的问题。（Ito 已经独立证明了相同的结果。）作为一个应用程序，我们使用高斯码计算通过至少 13 个交叉点的所有素数交替结的交叉帽数。