Ömür Deveci and Anthony G. Shannon

Notes on Number Theory and Discrete Mathematics

Print ISSN 1310–5132, Online ISSN 2367–8275

Volume 24, 2018, Number 4, Pages 26—37

DOI: 10.7546/nntdm.2018.24.4.26-37

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## Details

### Authors and affiliations

Ömür Deveci

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

Anthony G. Shannon

*Fellow, Warrane College, The University of New South Wales
Kensington 2033, Australia*

### Abstract

In this paper, we define the Redheffer numbers and then we obtain their miscellaneous properties. Also, we study the Redheffer numbers modulo *m*. Furthermore, we define the Redheffer orbits and the basic Redheffer orbits of 2-generator and 3-generator groups, then we examine the lengths of the periods of these orbits. Finally, we obtain the Redheffer lengths and the basic Redheffer lengths of some special finite groups as applications of Redheffer orbits and the basic Redheffer orbits.

### Keywords

- Redheffer numbers
- Matrix
- Sequence
- Group
- Length

### 2010 Mathematics Subject Classification

- 11B50
- 20F05
- 15A36
- 20D60

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## Cite this paper

Deveci, Ö., & Shannon, A. G. (2018). The Redheffer numbers and their applications. *Notes on Number Theory and Discrete Mathematics*, 24(4), 26-37, doi: 10.7546/nntdm.2018.24.4.26-37.