Recently, Dokos et al. conjectured that for all k,mβ₯1, the patterns 12β¦k(k+m+1)β¦(k+2)(k+1) and (m+1)(m+2)β¦(k+m+1)mβ¦21
are maj-Wilf-equivalent. In this paper, we confirm this conjecture for all
kβ₯1 and m=1. In fact, we construct a descent set preserving bijection
between 12β¦k(kβ1)-avoiding permutations and 23β¦k1-avoiding
permutations for all kβ₯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