Factorizations of some lower triangular matrices and related combinatorial identities

Cahit Köme
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 27, 2021, Number 4, Pages 207–218
DOI: 10.7546/nntdm.2021.27.4.207-218
Full paper (PDF, 264 Kb)

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Authors and affiliations

Cahit Köme
Department of Information Technology,
Nevşehir Hacı Bektaş Veli University
50300, Turkey

Abstract

In this study, we investigate the connection between second order recurrence matrix and several combinatorial matrices such as generalized r-eliminated Pascal matrix, Stirling matrix of the first and of the second kind matrices. We give factorizations and inverse factorizations of these matrices by virtue of the second order recurrence matrix. Moreover, we derive several combinatorial identities which are more general results of some earlier works.

Keywords

• Pascal matrix
• Stirling matrix
• Second order recurrence matrix
• Factorization
• Combinatorial identities

2020 Mathematics Subject Classification

• 15A23
• 11B39
• 05A10

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