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Apr 12, 2022 at 13:42 comment added Ben Deitmar ah, yes you're right. I got mixed up.
Apr 12, 2022 at 13:35 comment added Peter Taylor @Tardis, shouldn't it be $\binom{n-1}{n_1-1}$?
Apr 12, 2022 at 13:24 comment added Ben Deitmar small correction: we still need to multiply with $\frac{1}{2}{n \choose n_1}$, since for each spanning tree of $K_{n_1,n_2}$ the sets $U,W$ are always $\{1,...,n_1\}$ and $\{n_1+1,...,n\}$ respectively. We want to allow for $U$ to be any subset of $\{1,...,n\}$ with $n_1$ elements (thus the ${n \choose n_1}$ factor) but it still must contain $1$, thus the factor $\frac{1}{2}$.
Apr 12, 2022 at 13:02 vote accept Ben Deitmar
Apr 12, 2022 at 13:02 comment added Ben Deitmar Nice, an interesting approach. Thanks!
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