Self-dual interval orders and row-Fishburn matrices

Details Self-dual interval orders and row-Fishburn matrices Self-dual interval orders and row-Fishburn matrices

2011-11-21

arxiv.org/abs/1111.4723v1

Mathematics

Combinatorics

Scientific paper

Recently, Jel\'{i}nek 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 Jel\'{i}nek.

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