Minimal in terms of double-sided shadow subsets of Boolean cube layer distinct from circles

M. A. Bashov

Lomonosov Moscow State University, Moscow, Russia

Abstract: The double-shadow minimization problem in the Boolean cube layer is considered. The final lexicographical segment of the second layer is shown to have the minimal double-sided shadow. The minimal families of size $1+k(n-k)+(k-1)(n-k-1)$ in the $k$th layer are described when $n=2k$ for small values of $k$. Bibliogr. 5.

Keywords: shadow minimization, double-sided shadow, Boolean cube, ideal weight minimization.

UDC: 519.1

Received: 08.01.2012

 English version: Journal of Applied and Industrial Mathematics, 2013, 7:1, 29–40

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