Quasicyclic Symmetry and the Shannon Entropy

Abstract

In most of the axiomatic characterizations of the Shannon entropy, its two important properties, namely, total symmetry and recursivity, are widely used. In this paper, the authors have proposed a new property called “quasicyclic symmetry” which is weaker than symmetry in the strict sense. It is proved that quasicyclic symmetry and recursivity, taken together, are equivalent to total symmetry and recursivity.