Clebsch-Gordan coefficients: partitions of semi-magic squares of size three
Abstract: In the late 50s, Regge made remarkable connections between Clebsch-Gordan coefficients (CGCs) for SU(2) and semi-magic squares of size 3. We use the interplay of these subjects to obtain several new results: an elementary proof of MacMahon's formula for counting such squares with fixed line sum J, a generating function that counts the trivial zeros of CGCs, and a curious connection between the distribution of zeros of certain CGCS and prime numbers.