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We introduce vincular pattern posets, then we consider in particular thequasi-consecutive pattern poset, which is defined by declaring $\sigma \leq\tau$ whenever the permutation $\tau$ contains an occurrence of the permutation$\sigma$ in which all the entries are adjacent in $\tau$ except at most thefirst and the second. We investigate the M\"obius function of thequasi-consecutive pattern poset and we completely determine it for thoseintervals $[\sigma ,\tau ]$ such that $\sigma$ occurs precisely once in $\tau$.

Vincular pattern posets and the M\"obius function of the quasi-consecutive pattern poset