CONSTRUCTIONS OF REGULAR SPARSE ANTI-MAGIC SQUARES

For positive integers n and d with d < n, an n × n array A based on = {0, 1, ..., nd} is called a sparse anti-magic square of order n with density d, denoted by SAMS(n, d), if each non-zero element of X occurs exactly once in A, and its row-sums, column-sums and two main diagonal-sums constitute...

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Veröffentlicht in:Taehan Suhakhoe hoebo 2022, Vol.59 (3), p.617-642
Hauptverfasser: Chen, Guangzhou, Li, Wen, Xin, Bangying, Zhong, Ming
Format: Artikel
Sprache:kor
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Zusammenfassung:For positive integers n and d with d < n, an n × n array A based on = {0, 1, ..., nd} is called a sparse anti-magic square of order n with density d, denoted by SAMS(n, d), if each non-zero element of X occurs exactly once in A, and its row-sums, column-sums and two main diagonal-sums constitute a set of 2n + 2 consecutive integers. An SAMS(n, d) is called regular if there are exactly d non-zero elements in each row, each column and each main diagonal. In this paper, we investigate the existence of regular sparse anti-magic squares of order n ≡ 1, 5 (mod 6), and prove that there exists a regular SAMS(n, d) for any n ≥ 5, n ≡ 1, 5 (mod 6) and d with 2 ≤ d ≤ n - 1.
ISSN:1015-8634