<abstract xmlns="http://www.w3.org/1999/xhtml"><p>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.</p></abstract>

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.

Nonexistence of a Kruskal–Katona type theorem for double-sided shadow minimization in the Boolean cube layer

Acta Universitatis Sapientiae, Informatica

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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...

Nonexistence of a Kruskal–Katona type theorem for double-sided shadow minimization in the Boolean cube layer

Published Online: May 30, 2014

Page range: 53 - 62

Received: Feb 05, 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.