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.