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We employ the $1/2$-spin tautological relations to provide a particularcombinatorial identity. We show that this identity is a statement equivalent toFaber's formula for proportionalities of kappa-classes on $\mathcal{M}_g$,$g\geq 2$. We then prove several cases of the combinatorial identity, providinga new proof of Faber's formula for those cases.

Half-Spin Tautological Relations and Faber's Proportionalities of Kappa Classes