Nonexistence of a Kruskal–Katona type theorem for double-sided shadow minimization in the Boolean cube layer
| May 30, 2014
About this article
Published Online: May 30, 2014
Page range: 53 - 62
Received: Feb 05, 2013
DOI: https://doi.org/10.2478/ausi-2014-0004
© 2014
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A double-sided shadow minimization problem in the Boolean cube layer is investigated in this paper. The problem is to minimize the size of the union of the lower and upper shadows of a k-uniform family of subsets of [n]. It is shown that if 3 ⋜ k ⋜ n−3, there is no total order such that all its initial segments have minimal double-sided shadow.