an:07200529
Zbl 1434.60040
FĂ©ray, Valentin
Central limit theorems for patterns in multiset permutations and set partitions
EN
Ann. Appl. Probab. 30, No. 1, 287-323 (2020).
1050-5164 2168-8737
2020
j
60C05 60F05 05A05 05A18
combinatorial probability; central limit theorem; dependency graphs; patterns; multiset permutations; set partitions
Summary: We use the recently developed method of weighted dependency graphs to prove central limit theorems for the number of occurrences of any fixed pattern in multiset permutations and in set partitions. This generalizes results for patterns of size 2 in both settings, obtained by \textit{E. R. Canfield} et al. [Adv. Appl. Math. 46, No. 1--4, 109--124 (2011; Zbl 1227.05009)] and \textit{B. Chern} et al. [Adv. Appl. Math. 70, 92--105 (2015; Zbl 1327.60030)], respectively.
1227.05009; 1327.60030