Self-Dual Interval Orders and Row-Fishburn Matrices

Sherry H. F. Yan, Yuexiao Xu

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.

Keywords


self-dual interval order; self-dual Fishburn matrix; row-Fishburn matrix

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