Construction and enumeration of pandiagonal magic squares of order \(n\) from step method (Q2715957)
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scientific article; zbMATH DE number 1600929
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Construction and enumeration of pandiagonal magic squares of order \(n\) from step method |
scientific article; zbMATH DE number 1600929 |
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30 May 2001
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magic square
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enumeration
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step method
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0.88645095
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0.8663697
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Construction and enumeration of pandiagonal magic squares of order \(n\) from step method (English)
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A pandiagonal magic square (PMS) is an arrangement of the numbers \(0, 1, \ldots , n^2-1\) into an \(n\times n\) matrix such that all the sums of the entries in columns, rows, and extended diagonals (torus identification) are the same. The authors use the so-called step method, which is defined by a quadruple of integers \(1\leq a,b,c,d\leq n-1\) satisfying certain conditions, to construct a PMS for each \(n>3\) that is not of the form \(n=2m\), \(m\) odd. They enumerate, for \(n=8\) and \(n=9\), all (nonequivalent and having \(0\) as the top left entry) PMS's obtained by the method.
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