A320600 Let w = (w_1, w_2, ..., w_n) be a permutation of the integers {1, 2, ..., n}, and let f(k, w) be the length of the longest monotone subsequence of (w_k, w_{k+1}, ..., w_n) starting with w_k. Then a(n) is the number of permutations w in S_n such that Sum_{k=1..n} f(k,w) is minimized.
1, 2, 4, 4, 32, 156, 564, 1386, 1764
Offset: 1
Examples
For n = 4 the a(4) = 4 permutations are w_1 = (2,1,4,3), w_2 = (2,4,1,3), w_3 = (3,1,4,2), and w_4 = (3,4,1,2). In each case, f(1,w_i) + f(2,w_i) + f(3,w_i) + f(4,w_i) = A327672(4) = 7.
Links
- Sung Soo Kim, Problems and Solutions, Mathematics Magazine, 91:4 (2018), 310.
- Michael Reid, Problems and Solutions, Mathematics Magazine, 92:4 (2019), 314.
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