Abstract
We consider permutations avoiding a pattern of length three under the family of Mallows distributions. In particular, for any pattern (Formula presented.), we obtain rather precise results on the asymptotic probability as n → ∞ that a permutation (Formula presented.) under the Mallows distribution with parameter q ∈ (0, 1) avoids the pattern. By a duality between the parameters q and (Formula presented.), we also obtain rather precise results on the above probability for q > 1 and any pattern (Formula presented.).
| Original language | English |
|---|---|
| Article number | 4 |
| Pages (from-to) | 676-690 |
| Number of pages | 15 |
| Journal | Random Structures and Algorithms |
| Volume | 58 |
| Issue number | 4 |
| DOIs | |
| State | Published - Jul 2021 |
Keywords
- Mallows distribution
- pattern of length three
- pattern-avoiding permutation
- random permutation
All Science Journal Classification (ASJC) codes
- Software
- Applied Mathematics
- General Mathematics
- Computer Graphics and Computer-Aided Design