Hypomorphic Sperner systems and nonreconstructible functions

Abstract

A reconstruction problem is formulated for Sperner systems, and infinite families of nonreconstructible Sperner systems are presented. This has an application to a reconstruction problem for functions of several arguments and identification minors. Sperner systems being representations of certain monotone functions, infinite families of nonreconstructible functions are thus obtained. The clones of Boolean functions are completely classified in regard to reconstructibility.