Leo Betthauser, Ömür Deveci and Josh Hiller

Notes on Number Theory and Discrete Mathematics

Print ISSN 1310–5132, Online ISSN 2367–8275

Volume 27, 2021, Number 1, Pages 125–133

DOI: 10.7546/nntdm.2021.27.1.125-133

**Full paper (PDF, 181 Kb)**

## Details

### Authors and affiliations

Leo Betthauser

*Department of Mathematics, PO Box 118105, University of Florida
Gainesville, FL 32611-8105, United States
*

Ömür Deveci

*Department of Mathematics, Faculty of Science and Letters, Kafkas University
36100, Turkey
*

Josh Hiller

*Department of Mathematics and Computer Science, Adelphi University
New York, United States
*

### Abstract

We define the very general binomial matrix and find its eigendecomposition over arbitrary rings when such a decomposition is possible. Using this decomposition, we are able to compute the order of several varieties of Pascal’s matrices.

### Keywords

- Pascal’s matrix
- Binomial coefficients
- Matrix

### 2010 Mathematics Subject Classification

- 11B65
- 15A09
- 15A16

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## Cite this paper

Betthauser, L., Deveci, Ö., & Hiller, J. (2021). A very general binomial matrix. *Notes on Number Theory and Discrete Mathematics*, 27(1), 125-133, DOI: 10.7546/nntdm.2021.27.1.125-133.