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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 thesame number of filled cells $t$ in each column, filled with a certain set ofnumbers that is symmetric about the number zero, such that every row and columnhas a zero sum. We attempt to make progress toward a characterization of forwhich $(m, n, s, t)$ there exists such an array. This characterization iscomplete in the case where $n = s$ and in the case where $n = m$; we alsocharacterize three-fourths of the cases where $n = 2m$.

Existence of Some Signed Magic Arrays