Existence of some signed magic arrays. (English) Zbl 1440.05050
Summary: We consider the notion of a signed magic array, which is an \(m \times n\) rectangular array with the same number of filled cells \(s\) in each row and the same number of filled cells \(t\) in each column, filled with a certain set of numbers that is symmetric about the number zero, such that every row and column has a zero sum. We attempt to make progress toward a characterization of for which \((m, n, s, t)\) there exists such an array. This characterization is complete in the case where \(n = s\) and in the case where \(n = m\); we also characterize three-fourths of the cases where \(n=2m\).
MSC:
| 05B15 | Orthogonal arrays, Latin squares, Room squares |
References:
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