On a refinement of Wilf-equivalence for permutations
The electronic journal of combinatorics, Tome 22 (2015) no. 1
Recently, Dokos et al. conjectured that for all $k, m\geq 1$, the patterns $ 12\ldots k(k+m+1)\ldots (k+2)(k+1) $ and $(m+1)(m+2)\ldots (k+m+1)m\ldots 21$ are $maj$-Wilf-equivalent. In this paper, we confirm this conjecture for all $k\geq 1$ and $m=1$. In fact, we construct a descent set preserving bijection between $ 12\ldots k (k-1) $-avoiding permutations and $23\ldots k1$-avoiding permutations for all $k\geq 3$. As a corollary, our bijection enables us to settle a conjecture of Gowravaram and Jagadeesan concerning the Wilf-equivalence for permutations with given descent sets.
DOI :
10.37236/4465
Classification :
05A05, 05C30, 20B30
Mots-clés : \(maj\)-Wilf equivalent, pattern avoiding permutation, bijection
Mots-clés : \(maj\)-Wilf equivalent, pattern avoiding permutation, bijection
@article{10_37236_4465,
author = {Sherry H.F. Yan and Huiyun Ge and Yaqiu Zhang},
title = {On a refinement of {Wilf-equivalence} for permutations},
journal = {The electronic journal of combinatorics},
year = {2015},
volume = {22},
number = {1},
doi = {10.37236/4465},
zbl = {1307.05004},
url = {http://geodesic.mathdoc.fr/articles/10.37236/4465/}
}
Sherry H.F. Yan; Huiyun Ge; Yaqiu Zhang. On a refinement of Wilf-equivalence for permutations. The electronic journal of combinatorics, Tome 22 (2015) no. 1. doi: 10.37236/4465
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