Self-dual区间序与行-Fishburn矩阵
Self-dual interval orders and row-Fishburn matrices
摘要：
最近，Jelínek利用生成函数得到了降维$n$的自对偶区间阶数是降维$n$的行-Fishburn矩阵数的两倍.本文通过建立非负整数的上三角形矩阵的两个变形之间的双射，给出了这个关系的一个双射证明。使用双射，我们提供了一个组合证明的自对偶Fishburn矩阵和行-Fishburn矩阵之间的关系，回答了Jelínek提出的一个问题。
英文摘要：
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.
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