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- Matthias Beck, Moshe Cohen, Jessica Cuomo, Paul Gribelyuk
- The American Mathematical Monthly
- 2003

Magic squares have turned up throughout history, some in a mathematical context, others in philosophical or religious contexts. According to legend, the first magic square was discovered in China by an unknown mathematician sometime before the first century A.D. It was a magic square of order three thought to have appeared on the back of a turtle emerging… (More)

We define a semi-magic square to be a square matrix whose entries are nonnegative integers and whose rows and columns (that is, lines) sum up to the same number. A magic square is a semimagic square whose main diagonals also add up to the line sum. A symmetric magic square is a magic square which is a symmetric matrix. A pandiagonal magic square is a… (More)

- Jessica Cuomo, Nkiruka Nwasokwa, Vadim Ponomarenko
- Australasian J. Combinatorics
- 2005

A jump system is a set of lattice points satisfying a certain " two-step " axiom. A Manhattan set is the convex hull of a two-dimensional jump system. Taking multiple Manhattan sets, in layers, forms a three-dimensional object. We determine under what conditions this object is, in turn, a jump system.

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