Let n be a odd integer, and a permutation P of {1,2,...n} is called
1. dissipative if P(1) = 1 and P(n) = n
2. Morse if for each k = 1,2,...n, the number
k-1
i_k = Σ (-1)^(j+1) sign [ P^(-1)(j+1) - P^(-1)(j) ] ≧ 0
j=1
and i_1 = i_n = 0
where a*sign[a] = |a| for all nonzero a.
3. meander if for any two distinct 1 ≦ j,k ≦ n and j ≡ k (mod 2)
we have P^(-1)(k) is between P^(-1)(j) and P^(-1)(j+1),
then P^(-1)(k+1) is also between P^(-1)(j) and P^(-1)(j+1).
Question:
Find the total number of dissipative Morse meander permutations of n-elements.
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※ 編輯: tiwsjia 來自: 219.86.218.133 (07/02 01:49)