Self-dual interval orders and row-Fishburn matrices
Combinatorics
2011-11-22 v1
Abstract
Recently, Jel\'{i}nek derived that the number of self-dual interval orders of reduced size is twice the number of row-Fishburn matrices of size 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.
Keywords
Cite
@article{arxiv.1111.4723,
title = {Self-dual interval orders and row-Fishburn matrices},
author = {Sherry H. F. Yan and Yuexiao Xu},
journal= {arXiv preprint arXiv:1111.4723},
year = {2011}
}