The patterns of permutations

Herbert S. Wilf
2002 Discrete Mathematics  
Let n; k be positive integers, with k 6 n, and let be a ÿxed permutation of {1; : : : ; k}. 1 We will call the pattern. We will look for the pattern in permutations of n letters. A pattern is said to occur in a permutation if there are integers 1 6 i1 ¡ i2 ¡ · · · ¡ i k 6 n such that for all 1 6 r ¡ s 6 k we have (r) ¡ (s) if and only if (ir) ¡ (is). Example. Suppose = (132). Then this pattern of k = 3 letters occurs several times in the following permutation , of n = 14 letters (one such
more » ... ence is underlined): = (5 2 9 4 14 10 1 3 6 15 8 11 7 13 12):
doi:10.1016/s0012-365x(02)00515-0 fatcat:4mfhdis5abeeffwcw6jvxccfgm