On the distribution of coefficients of residue polynomials

TL;DR

This paper explores the distribution of coefficients in residue polynomials, using positive coefficient polynomials to generalize the combinatorial fact that half of all subsets of a finite set have even size, asymptotically.

Contribution

It introduces a polynomial formalism to generalize subset cardinality distribution properties asymptotically.

Findings

Half of all subsets of a finite set have even cardinality.

Asymptotic generalization of subset cardinality distribution.

Polynomial formalism effectively models combinatorial properties.

Abstract

Using the formalism of polynomials with positive coefficients, the fact that exactly half of all subsets of a finite set have even cardinality can be generalized asymptotically.