Asymptotic Behavior of Perturbations of Symmetric Functions.

In this paper we consider perturbations of symmetric Boolean functions $${{\sigma_{n,k_1}} +\ldots+{\sigma_{n,k_s}}}$$ in n-variable and degree k. We compute the asymptotic behavior of Boolean functions of the type for j fixed. In particular, we characterize all the Boolean functions of the type that are asymptotic balanced. We also present an algorithm that computes the asymptotic behavior of a family of Boolean functions from one member of the family. Finally, as a byproduct of our results, we provide a relation between the parity of families of sums of binomial coefficients. [ABSTRACT FROM AUTHOR]