Asymptotic behavior of perturbations of symmetric functions
In the paper [Electron. J. Comb. 18, No. 2, Research Paper P8, 21 p. (2011; Zbl 1250.11102)], the authors studied linear recurrences satisfied by sums of elementary symmetric Boolean functions, and used these recurrences to study the asymptotic behavior of these functions. In the current work, the authors extend these results to Boolean functions that are sums of a number of elementary symmetric functions and an arbitrary polynomial. The paper gives similar recurrence relations and draws conclusions about the asymptotic behavior as well, including classifying when such functions are asymptotically balanced. The authors also prove a result relating the parity of certain families of sums of binomial coefficients.
scientific article; zbMATH DE number 6339736
scientific article