Concerning the maximum size of the terms in the realization of symmetric functions

Abstract

One method for realizing symmetric functions uses terms which consist of sums of fundamental symmetric functions. In many situations these sums simplify considerably. It is shown that, in the worst case, the size of these sums could approach half the number of possible fundamental symmetric functions without any simplification being possible. An expression for the number of fundamental symmetric functions is derived. For three- and four-valued systems, the size of the largest disjunction of fundamental symmetric functions is shown, and these results are extrapolated to the general case. It appears that the ratio between the maximum size and the total number of fundamental symmetric functions rapidly approaches one-half.<>