Lattice path enumeration for semi-magic squares of size three
Robert Donley (New York)
Abstract: A semi-magic square is a square matrix consisting of non-negative integer entries and such that the sum along any row or column has the same value. For size three, MacMahon (1916) gave a formula for counting the number of such squares with a fixed line sum. We give a formula for the number of paths from 0 to a given semi-magic square M in the corresponding lattice. In turn, this reveals another formula for Clebsch-Gordan coefficients, which we use to give an efficient algorithm for deriving the 72 Regge symmetries.
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