A Metrization for Power-Sets with Applications to Combinatorial Analysis

Abstract

Combinatorial configurations may generally be phrased in terms of arrangements of objects into sets subject to certain conditions. In view of this, the question arises as to whether given a set S and its power-set Us (the class of all subsets of S), it might be possible to structure Us in a combinatorially significant manner. This paper proposes and investigates one such structuring achieved by defining a distance function over US.Given A, B in Us, define their distance bywhere N(E) denotes the number of elements in E, + ∞ being an admissible value.