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.

## 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 |
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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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