AbstractGiven k finite sets S1,…,Sk, to what extent is it possible to partition their union into two parts A and B in such a way that, for each j, Sj ∩ A and Sj ∩ B contain approximately the same number of elements? Bounds are found for this and similar questions
A set A is said to split a finite set B if exactly half the elements of B (up to rounding) are conta...
A set A is said to split a finite set B if exactly half the elements of B (up to rounding) are conta...
AbstractLet fk(n) denote the maximum of k-subsets of an n-set satisfying the condition in the title....
AbstractGiven k finite sets S1,…,Sk, to what extent is it possible to partition their union into two...
AbstractBounds are obtained on the number of subsets in a family of subsets of an n element set whic...
AbstractLet n, t, k be integers, n ⩾ t ⩾ 1, k ⩾ 2. Let x = {1, 2, …, n}. Let F be a family of subset...
AbstractThe principal result of this paper establishes the validity of a conjecture by Graham and Ro...
AbstractLet S be an n-element set. In this paper, we determine the smallest number f(n) for which th...
AbstractIf X is an n-element set, we call a family G⊂PX a k-generator for X if every x⊂X can be expr...
AbstractLet X = X1 ∪ X2, X1 ∩ X2 = 0 be a partition of an n-element set. Suppose that the family F o...
Given a finite . n-element set . X, a family of subsets . F⊂2X is said to . separate X if any two el...
Some best possible inequalities are established for k-partition free families (cf. Definition 1) and...
AbstractLet H be a finite set, and A1, A2, …, Am subsets of H. We call a system A separating system,...
Given a finite n-element set X, a family of subsets F ⊂ 2^X is said to separate X if any two element...
Given a finite n-element set X, a family of subsets F ⊂ 2X is said to separate X if any two element...
A set A is said to split a finite set B if exactly half the elements of B (up to rounding) are conta...
A set A is said to split a finite set B if exactly half the elements of B (up to rounding) are conta...
AbstractLet fk(n) denote the maximum of k-subsets of an n-set satisfying the condition in the title....
AbstractGiven k finite sets S1,…,Sk, to what extent is it possible to partition their union into two...
AbstractBounds are obtained on the number of subsets in a family of subsets of an n element set whic...
AbstractLet n, t, k be integers, n ⩾ t ⩾ 1, k ⩾ 2. Let x = {1, 2, …, n}. Let F be a family of subset...
AbstractThe principal result of this paper establishes the validity of a conjecture by Graham and Ro...
AbstractLet S be an n-element set. In this paper, we determine the smallest number f(n) for which th...
AbstractIf X is an n-element set, we call a family G⊂PX a k-generator for X if every x⊂X can be expr...
AbstractLet X = X1 ∪ X2, X1 ∩ X2 = 0 be a partition of an n-element set. Suppose that the family F o...
Given a finite . n-element set . X, a family of subsets . F⊂2X is said to . separate X if any two el...
Some best possible inequalities are established for k-partition free families (cf. Definition 1) and...
AbstractLet H be a finite set, and A1, A2, …, Am subsets of H. We call a system A separating system,...
Given a finite n-element set X, a family of subsets F ⊂ 2^X is said to separate X if any two element...
Given a finite n-element set X, a family of subsets F ⊂ 2X is said to separate X if any two element...
A set A is said to split a finite set B if exactly half the elements of B (up to rounding) are conta...
A set A is said to split a finite set B if exactly half the elements of B (up to rounding) are conta...
AbstractLet fk(n) denote the maximum of k-subsets of an n-set satisfying the condition in the title....
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