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- Title
On a Conjecture About Strong Pattern Avoidance.
- Authors
Pan, Junyao
- Abstract
In 2019, Bóna and Smith introduced the definition of strong pattern avoidance, that is, a permutation π strongly avoids a pattern σ if π and π 2 both avoid σ . Let S A v n (σ 1 , σ 2 ,... , σ r) denote the set of permutations in S n that strongly avoid the patterns σ 1 , σ 2 ,... , σ r . In this note, we prove that | S A v n (321 , 1342) | = 2 F n + 2 - n - 2 for every positive integer n, where F n is the n-th Fibonacci number under the initial conditions F 1 = F 2 = 1 . This gives an affirmative answer to a conjecture proposed by Burcroff and Defant.
- Publication
Graphs & Combinatorics, 2023, Vol 39, Issue 1, p1
- ISSN
0911-0119
- Publication type
Article
- DOI
10.1007/s00373-022-02602-y