Sim, Kai An and Wong, Kok Bin (2021) Magic square and arrangement of consecutive integers that avoids k-term arithmetic progressions. Mathematics, 9 (18). ISSN 2227-7390, DOI https://doi.org/10.3390/math9182259.
Full text not available from this repository.Abstract
In 1977, Davis et al. proposed a method to generate an arrangement of n]={1,2, horizontal ellipsis ,n} that avoids three-term monotone arithmetic progressions. Consequently, this arrangement avoids k-term monotone arithmetic progressions in n] for k >= 3. Hence, we are interested in finding an arrangement of n] that avoids k-term monotone arithmetic progression, but allows k-1-term monotone arithmetic progression. In this paper, we propose a method to rearrange the rows of a magic square of order 2k-3 and show that this arrangement does not contain a k-term monotone arithmetic progression. Consequently, we show that there exists an arrangement of n consecutive integers such that it does not contain a k-term monotone arithmetic progression, but it contains a k-1-term monotone arithmetic progression.
| Item Type: | Article |
|---|---|
| Funders: | Fundamental Research Grant Scheme (FRGS) by Malaysia Ministry of Higher Education and Publication Support Scheme by Sunway University, Malaysia (FRGS/1/2020/STG06/SYUC/03/1) |
| Uncontrolled Keywords: | Magic square; Arithmetic progression; Permutations |
| Subjects: | Q Science > QA Mathematics |
| Divisions: | Faculty of Science > Institute of Mathematical Sciences |
| Depositing User: | Ms Zaharah Ramly |
| Date Deposited: | 09 Jun 2022 06:49 |
| Last Modified: | 09 Jun 2022 06:49 |
| URI: | http://eprints.um.edu.my/id/eprint/27570 |
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