1 citations · 1 across the 5 of their papers we have counts for
5 papers
Using binary string to prove the Collatz conjecture
Jishe Feng
We introduce a full binary directed tree structure to represent the set of natural numbers, further categorizing them into three distinct subsets: pure odd numbers, pure even numbe…
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…
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…
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…
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…