Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Two deformed Pascal's triangles and its new properties   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.

21
The categories of this paper are: adap-org
29
The categories of this paper are: funct-an
13
The categories of this paper are: quant-ph
25
The categories of this paper are: patt-sol
26
The categories of this paper are: bayes-an
8
The categories of this paper are: hep-ex
7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg
24
The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th
15
The categories of this paper are: nucl-ex
1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
20
The categories of this paper are: acc-phys
6
The categories of this paper are: astro-ph
3
The categories of this paper are: physics