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Hypomorphic Sperner systems and non-reconstructible functions

Couceiro, Miguel; Lehtonen, Erkko; Schölzel, Karsten

Order, 32 (2015), 255–292

A reconstruction problem is formulated for Sperner systems, and infinite families of non-reconstructible 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 non-reconstructible functions are thus obtained. The clones of Boolean functions are completely classified in regard to reconstructibility.