Recently Chen-Liang-Wang (Linear Algerbra Appl. 471 (2015) 383—393) proved some sufficient conditions for the total positivity of Catalan-Stieltjes matrices. Our aim is to provide a combinatorial interpretation of their sufficiant conditions. More precisely, for any Catalan-Stieltjes matrix $A$ we construct a digraph with a weight, which is positive under their sufficient conditions, such that every minor of $A$ is equal to the sum of weights of families of nonintersecting paths of the digraph. We have also an analogue result for the minors of Hankel matrix associated to the first column of Catalan-Stieltjes matrix $A$.
@article{10_37236_6270,
author = {Qiongqiong Pan and Jiang Zeng},
title = {On total positivity of {Catalan-Stieltjes} matrices},
journal = {The electronic journal of combinatorics},
year = {2016},
volume = {23},
number = {4},
doi = {10.37236/6270},
zbl = {1351.05041},
url = {http://geodesic.mathdoc.fr/articles/10.37236/6270/}
}
TY - JOUR
AU - Qiongqiong Pan
AU - Jiang Zeng
TI - On total positivity of Catalan-Stieltjes matrices
JO - The electronic journal of combinatorics
PY - 2016
VL - 23
IS - 4
UR - http://geodesic.mathdoc.fr/articles/10.37236/6270/
DO - 10.37236/6270
ID - 10_37236_6270
ER -
%0 Journal Article
%A Qiongqiong Pan
%A Jiang Zeng
%T On total positivity of Catalan-Stieltjes matrices
%J The electronic journal of combinatorics
%D 2016
%V 23
%N 4
%U http://geodesic.mathdoc.fr/articles/10.37236/6270/
%R 10.37236/6270
%F 10_37236_6270
Qiongqiong Pan; Jiang Zeng. On total positivity of Catalan-Stieltjes matrices. The electronic journal of combinatorics, Tome 23 (2016) no. 4. doi: 10.37236/6270
