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게시글 주소: https://orbi.kr/00039504468
Q : If $\tau_i\in S_n$ are transpositions s.t. $\langle\tau_1,...,\tau_k\rangle = S_n$ then $k\geq n-1$.
S P : Suppose not. Join the vertices $1,...,n$ with the edges corresponding to transpositions $\tau_i$, we get a graph with $n$ vertices and $<n-1$ edges so the graph is not connected.
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