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A central limit theorem for vincular permutation patterns. (English) Zbl 1401.05013
Summary: We study the number of occurrences of any fixed vincular permutation pattern. We show that this statistics on uniform random permutations is asymptotically normal and describe the speed of convergence. To prove this central limit theorem, we use the method of dependency graphs. The main difficulty is then to estimate the variance of our statistics. We need a lower bound on the variance, for which we introduce a recursive technique based on the law of total variance.

MSC:
05A05 Permutations, words, matrices
05C99 Graph theory
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