Derangement permutation r of [n] i∈[m,π()卡i "permutations with no fixed point" !n U=Sn symmetric group A,={π|π(i)=i} ∩A=∑(-1)川|A IEIn] Ar={πi∈I,π()=} Ar=(m-I)月U = Sn Derangement ⇤i ￾ [n], ￾(i) ⇥= i permutation ￾ of [n] “permutations with no fixed point” Ai = {￾ | ￾(i) = i} AI = {￾ | ⇥i ￾ I, ￾(i) = i} |AI | = (n ￾ |I|)! ￾ I￾[n] (￾1)|I| |AI | ￾ ￾ ￾ ￾ ￾ ￾ ￾ i￾[n] Ai ￾ ￾ ￾ ￾ ￾ ￾ = symmetric group !n