PC Seminar: Limit theorems for Fishburn matrices

Abstract: Fishburn matrices are upper-triangular square matrices with nonnegative integers as entries such that no row and no column contains exclusively zeros. They have been found to be bijectively equivalent to several other combinatorial structures such as (2+2)-free posets, ascent sequences, certain pattern avoiding permutations, (2-1)-avoiding inversion sequences, Stoimenow matchings, and regular linearized chord diagrams. In addition to their rich combinatorial connections and modeling capabilities, the corresponding asymptotic enumeration and the finer distributional properties are equally enriching and challenging. We present a general, direct, analytic approach for dealing with the asymptotic enumeration and stochastic properties on generalized Fishburn matrices. Many normal and Poisson limit laws are given, and they represent the first of their kinds. This talk is based on joint work with Emma Yu Jin and Michael Schlosser.

PS our papers on Fishburn matrices

This is a seminar in our seminar series on Probability and Combinatorics (PC).