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In the theory of Clebsch-Gordan coefficients, one may recognize the domainspace as the set of weakly semi-magic squares of size three. Two partitions onthis set are considered: a triangle-hexagon model based on top lines, and onebased on the orbits under a finite group action. In addition to giving anotherproof of McMahon's formula, we give a generating function that counts theso-called trivial zeros of Clebsch-Gordan coefficients and its associatedquasi-polynomial.

Partitions for semi-magic squares of size three