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Patterns in random permutations avoiding the pattern 321
Author(s) -
Janson Svante
Publication year - 2019
Publication title -
random structures and algorithms
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.314
H-Index - 69
eISSN - 1098-2418
pISSN - 1042-9832
DOI - 10.1002/rsa.20806
Subject(s) - random permutation , excursion , mathematics , permutation (music) , limit (mathematics) , combinatorics , brownian excursion , scaling limit , scaling , derangement , set (abstract data type) , brownian motion , statistical physics , discrete mathematics , computer science , statistics , physics , mathematical analysis , geometry , block (permutation group theory) , geometric brownian motion , diffusion process , knowledge management , innovation diffusion , political science , acoustics , law , programming language
We consider a random permutation drawn from the set of 321 ‐avoiding permutations of length n and show that the number of occurrences of another pattern σ has a limit distribution, after scaling by n m + ℓ where m is the length of σ and ℓ is the number of blocks in it. The limit is not normal, and can be expressed as a functional of a Brownian excursion.