“…Fishburn matrices, introduced in the 1970s in the context of interval orders (in order theory) and directed graphs (see [1,18,23,41]), are nonnegative, upper-triangular ones without zero row or column. They have later found to be bijectively equivalent to several other combinatorial structures such as (2 + 2)-free posets, ascent sequences, pattern-avoiding permutations, patternavoiding inversion sequences, Stoimenow matchings, and regular chord diagrams; see, for instance, [6,14,21,30,35] and Section 2 for more information. In addition to their rich combinatorial connections, the corresponding asymptotic enumeration and the finer distributional properties are equally enriching and challenging, as we will explore in this paper.…”