In this paper, we derive many new identities on the classical Catalan triangle $\mathcal{C}=(C_{n,k})_{n\geq k\geq 0}$, where $C_{n,k}=\frac{k+1}{n+1}\binom{2n-k}{n}$ are the well-known ballot numbers. The first three types are based on the determinant and the fourth is relied on the permanent of a square matrix. It not only produces many known and new identities involving Catalan numbers, but also provides a new viewpoint on combinatorial triangles.
@article{10_37236_3701,
author = {Yidong Sun and Fei Ma},
title = {Some new binomial sums related to the {Catalan} triangle},
journal = {The electronic journal of combinatorics},
year = {2014},
volume = {21},
number = {1},
doi = {10.37236/3701},
zbl = {1300.05041},
url = {http://geodesic.mathdoc.fr/articles/10.37236/3701/}
}
TY - JOUR
AU - Yidong Sun
AU - Fei Ma
TI - Some new binomial sums related to the Catalan triangle
JO - The electronic journal of combinatorics
PY - 2014
VL - 21
IS - 1
UR - http://geodesic.mathdoc.fr/articles/10.37236/3701/
DO - 10.37236/3701
ID - 10_37236_3701
ER -
%0 Journal Article
%A Yidong Sun
%A Fei Ma
%T Some new binomial sums related to the Catalan triangle
%J The electronic journal of combinatorics
%D 2014
%V 21
%N 1
%U http://geodesic.mathdoc.fr/articles/10.37236/3701/
%R 10.37236/3701
%F 10_37236_3701
Yidong Sun; Fei Ma. Some new binomial sums related to the Catalan triangle. The electronic journal of combinatorics, Tome 21 (2014) no. 1. doi: 10.37236/3701
