On a refinement of Wilf-equivalence for permutations

الأصل · EN

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