Analyzing, Visualizing, and Searching for small size Balanced sets

Abstract

We describe the design and implementation of a computer application that can search for a small size balanced set modulo p, with p prime. Additionally, the application can”analyze” and ”visualize” any given balanced set to show graphically the dependancies between the elements of the set. A nonempty set S of residues modulo N is balanced if for each x ∈ S, there is a d with 0 <d ≤ N/2 such that x ± d mod N both lie in S; we use α(N) to denote the minimum cardinality of a balanced set modulo N. Small size balanced sets are needed for a winning strategy in the Vector game which was introduced together with balanced sets in [5] .