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

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

A combinatorial identity

We give an elementary proof of an interesting combinatorial identity which is of particular interest in graph theory and its applications

A combinatorial identity for studying Sato-Tate type problems

We derive a combinatorial identity which is useful in studying the distribution of Fourier coefficients of L-functions by allowing us to pass from knowledge of moments of the coefficients to the distribution of the coefficients.Comment: This paper contains the proof of a combinatorial identity used to study effective equidistribution laws for the Fourier coefficients of elliptic curve L-functions investigated by the first two authors in http://arxiv.org/abs/1004.275