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The patterns of permutations
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
doi:10.1016/s0012-365x(02)00515-0
fatcat:4mfhdis5abeeffwcw6jvxccfgm