3 papers
math.GM2020
The explicit formula of Hankel determinant with Catalan elements
Jishe Feng
Applying Johann Cigler's Hankel determinant formula in terms of the binomial coefficient determinants, which is simplified from Christian Krattenthale's, we get an explicit formula…
math.CO2019
Two deformed Pascal's triangles and its new properties
Jishe Feng, Cunqin Shi, Huani Zhao
In this paper, firstly, by a determinant of deformed Pascal's triangle, namely the normalized Hessenberg matrix determinant, to count Dyck paths, we give another combinatorial proo…
math.CO2018
The Hessenberg matrices and Catalan and its generalized numbers
Jishe Feng
We present determinantal representations of the Catalan numbers, k-Fuss-Catalan numbers, and its generalized number. The entries of the normalized Hessenberg matrices are the binom…