Algebraic Combinatorics of Magic Squares

Details Algebraic Combinatorics of Magic Squares Algebraic Combinatorics of Magic Squares

2004-05-25

arxiv.org/abs/math/0405476v1

Mathematics

Combinatorics

Ph.D. Thesis

Scientific paper

We describe how to construct and enumerate Magic squares, Franklin squares, Magic cubes, and Magic graphs as lattice points inside polyhedral cones using techniques from Algebraic Combinatorics. The main tools of our methods are the Hilbert Poincare series to enumerate lattice points and the Hilbert bases to generate lattice points. We define polytopes of magic labelings of graphs and digraphs, and give a description of the faces of the Birkhoff polytope as polytopes of magic labelings of digraphs.

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