@article{Halıcı2025, 
author = {Serpil Halıcı and Zehra Betül Gür},
title = {On some combinatorial identities related to super Catalan matrix},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {7},
pages = {16139-16156},
keywords = {super Catalan numbers, LU-decomposition, Cholesky decomposition, Lucas polynomials},
url = {https://www.sciopen.com/article/10.3934/math.2025723},
doi = {10.3934/math.2025723},
abstract = {In this paper, we define a new matrix        S          n       constructed by super Catalan numbers. Also, we give Cholesky and LU-decompositions, Hermite normal form, and the determinant of the matrix        S          n      . Moreover, we derive auxiliary results involving some summation formulas via the coefficients of Lucas polynomials and scaled coefficients of Chebyshev polynomials. Additionally, we give a matrix                      S        ´                    n       by modifying the matrix        S          n       to deduce a matrix identity related to matrices        S          n       and                      S        ´                    n        . By using the decomposition method, we give an application of solving a system of linear equations of order    n with coefficients    S  (  m  ,  n  ) and find a general solution.}
}