Year: 2019
Type: preprint
Abstract: 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 proof of the theorems which are of Catalan numbers determinant representations and the recurrence formula. Secondly, a determinant of normalized Toeplitz-Hessenberg matrix, whose entries are binomials, arising in power series, we derive new four properties of Pascal's triangle.
Source: arXiv (Cornell University)
Authors: Feng, Jishe, Shi, Cunqin, Zhao, Huani
Institution: Longdong University
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3088116152