Wilf equivalences between vincular patterns in inversion sequences

Inversion sequences are finite of non-negative integers, where the value each entry is bounded from above by its position. They provide a useful encoding permutations. Patterns in inversion have been studied Corteel–Martinez–Savage–Weselcouch and Mansour–Shattuck classical case, patterns can occur any positions, Auli–Elizalde consecutive only adjacent entries form an occurrence pattern. These papers classify length 3 into Wilf equivalence classes according to number avoiding them. In this paper we consider vincular sequences, which, analogy Babson–Steingrímsson permutations, require certain be adjacent, thus generalize both patterns. Solving three conjectures Lin Yan, complete classification classes, more restrictive that occurrences pattern positions such occurrences. We find first known instance these two do not coincide.