Subsets in a Boolean cube layer which are minimal by double-sided shadow and distinct from disks

摘要

We consider the double-shadow minimization problem in a Boolean cube layer. It is proved that a right lexicographic segment of the second layer has the minimal double-sided shadow. The minimal families of size 1 + k(n - k) + (k - 1)(n - k - 1) in the kth layer are described when n = 2k and for small values of k.