Nonexistence of a Kruskal–Katona type theorem for double-sided shadow minimization in the Boolean cube layer
| 30 mag 2014
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Pubblicato online: 30 mag 2014
Pagine: 53 - 62
Ricevuto: 05 feb 2013
DOI: https://doi.org/10.2478/ausi-2014-0004
© 2014
This article is distributed under the terms of the Creative Commons Attribution Non-Commercial License, which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.