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A. Kasraoui

# New Wilf-equivalence results for dashed patterns

**Abstract.** We give a sufficient condition for the two dashed patterns $\tau^{(1)}-\tau^{(2)}-\cdots-\tau^{(\ell)}$
and $\tau^{(\ell)}-\tau^{(\ell-1)}-\cdots-\tau^{(1)}$ to be (strongly) Wilf-equivalent. This permits to solve in a unified
way several problems of Heubach and Mansour on Wilf-equivalences on words and compositions, as well as a conjecture of Baxter
and Pudwell on Wilf-equivalences on permutations. We also give a better explanation of the equidistribution of the parameters
$\MAK+\bMAJ$ and $\MAK'+\bMAJ$ on ordered set partitions. These results can be viewed as consequences of a simple proposition
which states that the set valued statistics "descent set'' and "rise set'' are equidistributed over each equivalence class of
the partially commutative monoid generated by a poset $(X,\leq)$.

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