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Ito-Takimura recently defined a splice-unknotting number $u^-(D)$ for knotdiagrams. They proved that this number provides an upper bound for the crosscapnumber of any prime knot, asking whether equality holds in the alternatingcase. We answer their question in the affirmative. (Ito has independentlyproven the same result.) As an application, we compute the crosscap numbers ofall prime alternating knots through at least 13 crossings, using Gauss codes.

Crosscap numbers of alternating knots via unknotting splices