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.