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.
@article{10_37236_2201,
author = {Sherry H. F. Yan and Yuexiao Xu},
title = {Self-dual interval orders and {row-Fishburn} matrices},
journal = {The electronic journal of combinatorics},
year = {2012},
volume = {19},
number = {2},
doi = {10.37236/2201},
zbl = {1243.05015},
url = {http://geodesic.mathdoc.fr/articles/10.37236/2201/}
}
TY - JOUR
AU - Sherry H. F. Yan
AU - Yuexiao Xu
TI - Self-dual interval orders and row-Fishburn matrices
JO - The electronic journal of combinatorics
PY - 2012
VL - 19
IS - 2
UR - http://geodesic.mathdoc.fr/articles/10.37236/2201/
DO - 10.37236/2201
ID - 10_37236_2201
ER -
%0 Journal Article
%A Sherry H. F. Yan
%A Yuexiao Xu
%T Self-dual interval orders and row-Fishburn matrices
%J The electronic journal of combinatorics
%D 2012
%V 19
%N 2
%U http://geodesic.mathdoc.fr/articles/10.37236/2201/
%R 10.37236/2201
%F 10_37236_2201
Sherry H. F. Yan; Yuexiao Xu. Self-dual interval orders and row-Fishburn matrices. The electronic journal of combinatorics, Tome 19 (2012) no. 2. doi: 10.37236/2201
