a magic (p x q)-rectangle. c>~O. inequality 2c +4 ~< (n- 1 )2 holds. Moreover, these centrally symmetric rectangles can be constructed in such a way that in each row the absolute difference between the number of the positive entries and the number of the negative entries is equal to 1.
In this paper we solve the problem of the existence of centrally symmetric and magic rectangles by determining all pairs of integers (n, c) resp. (p, q), for ...
Proposition 1. If a balanced centrally symmetric (m; n)-rectangle exists; then a magic (m; n)-rectangle exists. Proposition 2. If balanced centrally symmetric ...
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—Magic rectangles are a classical generalization of the well-known magic squares, and they are related to graphs. A graph G is called degree-magic if there ...
Centrally symmetric and magic rectangles. Authors: Thomas Bier. Thomas Bier ... Centrally symmetric and magic rectangles. Mathematics of computing.
It is centre-complementary if the sum of any pair of centrally symmetric positions is constant. As a natural generalization of symmetric magic squares, centre- ...
Centrally symmetric rectangles have the property that they can be added together or to magic rectangles to form larger rectangles of the same type. Theorem 2 ...
Oct 31, 2024 · Magic rectangles are a natural generalization of magic squares. Let a and b be positive integers. A magic rectangle MR(a, b) is an a × b array ...
Jun 1, 2024 · The center 4x4 square can be any center of an even concentric magic square of the same order including any aspect of the 880 order 4 squares.
Oct 31, 2024 · Following the work by Bier and Rogers [2] , Bier and Kleinschmidt [1] provided a simple proof for Theorem 1.1 by utilizing centrally symmetric ...
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