Nonexistence of a Kruskal–Katona type theorem for double-sided shadow minimization in the Boolean cube layer
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چکیده
منابع مشابه
Nonexistence of a Kruskal–Katona type theorem for double-sided shadow minimization in the Boolean cube layer
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. Denote by ([n] k ) the family of all subsets of t...
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Friedgut-Kalai-Naor Theorem for Slices of the Boolean Cube
The Friedgut–Kalai–Naor theorem, a basic result in the field of analysis of Boolean functions, states that if a Boolean function on the Boolean cube {0,1}n is close to a function of the form c0 +∑i cixi, then it is close to a dictatorship (a function depending on a single coordinate). We prove an analogous theorem for functions defined on the slice ([n] k ) = {(x1, . . . ,xn) ∈ {0,1}n : ∑i xi =...
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Nonexistence of a Kruskal-Katona Type Theorem for Subword Orders
We consider the poset SO(n) of all words over an n{element alphabet ordered by the subword relation. It is known that SO(2) falls into the class of Macaulay posets, i.e. there is a theorem of Kruskal{Katona type for SO(2). As the corresponding linear ordering of the elements of SO(2) the vip{order can be chosen. Daykin introduced the V {order which generalizes the vip{order to the n 2 case. He ...
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ژورنال
عنوان ژورنال: Acta Universitatis Sapientiae, Informatica
سال: 2013
ISSN: 2066-7760
DOI: 10.2478/ausi-2014-0004