Patterns of relation triples in inversion and ascent sequences

摘要

Recently, Martinez and Savage carried out the systematic study of inversion sequences avoiding triples of relations. They reported many nice connections with familiar combinatorial families and posed several enumeration conjectures. All of their conjectures have already been solved except those related to the OEIS sequence A098746. In this paper, we address those remaining conjectures, which completes a picture for all the suspected connections arising in their investigation.