Self-Dual Interval Orders and Row-Fishburn Matrices

Abstract

Recently, Jelínek derived  that the number of self-dual interval orders of reduced size $n$ is twice the number of row-Fishburn matrices of size $n$ by using generating functions. In this paper, we present a bijective proof of this relation by establishing a bijection between two variations of upper-triangular matrices of nonnegative integers. Using the bijection, we provide a combinatorial proof  of the refined relations between self-dual Fishburn matrices and row-Fishburn matrices in answer to a problem proposed by Jelínek.