On a Refinement of Wilf-equivalence for Permutations

Sherry H.F. Yan, Huiyun Ge, Yaqiu Zhang
2015 Electronic Journal of Combinatorics  
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
more » ... ure of Gowravaram and Jagadeesan concerning the Wilf-equivalence for permutations with given descent sets.
doi:10.37236/4465 fatcat:vefikn3ytzdlrlvnjzdhnr2spq