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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★ 1 cited
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…
math.CO2016
Matrices about the lattice paths
Jishe Feng
From the matrix point of view, we use the recursion to discuss four combinatorial numbers in terms of the integer lattice paths, this is different from Andrá's method (Andra). We g…