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Masters Thesis
Magic counting with inside-out polytopes
In this paper, we investigate strong 4 x 4 pandiagonal magic squares (no entries repeat; equal row sums, column sums, and diagonal sums, including the wrap-around ones), strong 5 x 5 pandiagonal magic squares, weak 2 x n magic rectangles (repeating entries allowed; equal row sums and equal column sums), and 2 x n magilatin rectangles (no entries repeat in a row/column; equal row sums and equal column sums). The magic counts depend on the magic sum or the upper bound of the entries. We compute their counting quasipolynomials and the associated generating functions by using a geometrical interpretation of the problems, considering them as counting the lattice points in polytopes with removed hyperplanes.
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