Say that a permutation 7 on [2n] has property P if for some i [2n],...

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Say that a permutation 7 on [2n] has property P if for some i € [2n], |πT (i) π(i+1)| = n, where i + 1 is taken modulo 2. Show that, for each n, there are more permutations with property P than without it. Hint: Consider the sets A₂ = {T: |n(i)−π(i+1)| = n}. Show that |A₁| = 2n(2n−2)! and A¿ÑAi+¹ - = 0. = Say that a permutation 7 on [2n] has property P if for some i € [2n], |πT (i) π(i+1)| = n, where i + 1 is taken modulo 2. Show that, for each n, there are more permutations with property P than without it. Hint: Consider the sets A₂ = {T: |n(i)−π(i+1)| = n}. Show that |A₁| = 2n(2n−2)! and A¿ÑAi+¹ - = 0. =