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

We introduce vincular pattern posets, then we consider in particular the quasi-consecutive pattern poset, which is defined by declaring $\sigma \leq \tau$wheneverthepermutation$\tau$containsanoccurrenceofthepermutation$\sigma$inwhichalltheentriesareadjacentin$\tau$ except at most the first and the second. We investigate the M"obius function of the quasi-consecutive pattern poset and we completely determine it for those intervals $[\sigma ,\tau ]$ such that $\sigma$ occurs precisely once in $\tau$.