Super Symmetry

Abstract

Super symmetry is a type of matrix-based symmetry that extends the concept of total symmetry. Super symmetric functions are “even more symmetric” than totally symmetric functions. Even if a function is not super symmetric, the super symmetric transpose matrices can be used to detect partial super symmetries. These partial symmetries can be mixed arbitrarily with ordinary symmetric variable pairs to create large sets of mutually symmetric variables. In addition, one can detect subsets of super symmetric inputs, which are distinct from partial super symmetries. Super symmetry allows many new types of Boolean function symmetry to be detected and exploited.