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A reconstruction problem is formulated for Sperner systems, and infinitefamilies of nonreconstructible Sperner systems are presented. This has anapplication to a reconstruction problem for functions of several arguments andidentification minors. Sperner systems being representations of certainmonotone functions, infinite families of nonreconstructible functions are thusobtained. The clones of Boolean functions are completely classified in regardto reconstructibility.

Hypomorphic Sperner systems and nonreconstructible functions