Anyone know how to do a combinatorial proof for this stirling number of second kind $S(m,m-1) = \frac{m(m-1)}{2}$ for all integers $m\geq$ 1. Thanks in advance. $S(m,n)$ denote that the set of all partitions of $\{1,...,m\}$ into exactly $n$ non-empty subsets.
2026-03-26 01:28:37.1774488517
Combinatorial proof for this stirling number of second kind
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You have $m$ elements and $m-1$ boxes. This means that exactly one box has to contain exactly $2$ elements. Can you take it from here?