Patterns in random permutations avoiding the pattern 321 | Zendy

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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.

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