AbstractA family of sets has the equal union property if and only if there exist two nonempty disjoint subfamilies having the same union. We prove that any n nonempty subsets of an n-element set have the equal union property if the sum of their cardinalities exceeds n(n+1)/2. This bound is tight. Among families in which the sum of the cardinalities equals n(n+1)/2, we characterize those having the equal union property
International audienceWe consider the problem of minimizing the size of a family of sets G such that...
An old problem of Moser asks: what is the size of the largest union-free subfamily that one can guar...
Given a family F of subsets of [n], we say two sets A,B ∈ F are comparable if A ⊂ B or B ⊂ A. Sperne...
AbstractA family of sets has the equal union property if and only if there exist two nonempty disjoi...
Let F[subscript 1] and F[subscript 2] be two families of subsets of an n-element set. We say that F[...
: Following Frankl and Furedi [1] we say a family, F , of subsets of an n-set is weakly union-free i...
AbstractWe present a conjecture, with some supporting results, concerning the maximum size of a fami...
AbstractA union-closed family F is a finite collection of sets not all empty, such that any union of...
A family of sets is union-closed if it contains the union of any two of its elements. Reimer (2003) ...
AbstractA family of nonempty sets has the equal union property if there exist two nonempty disjoint ...
Given a set S of n integers, the problem is to decide whether there exist two disjoint nonempty subs...
AbstractA union closed familyAis a finite family of sets such that the union of any two sets inAis a...
AbstractA family F of k-subsets of an n-set X is disjoint union-free (DUF) if all disjoint pairs of ...
AbstractWe consider the maximal size of families of k-element subsets of an n element set [n] that s...
AbstractGiven k finite sets S1,…,Sk, to what extent is it possible to partition their union into two...
International audienceWe consider the problem of minimizing the size of a family of sets G such that...
An old problem of Moser asks: what is the size of the largest union-free subfamily that one can guar...
Given a family F of subsets of [n], we say two sets A,B ∈ F are comparable if A ⊂ B or B ⊂ A. Sperne...
AbstractA family of sets has the equal union property if and only if there exist two nonempty disjoi...
Let F[subscript 1] and F[subscript 2] be two families of subsets of an n-element set. We say that F[...
: Following Frankl and Furedi [1] we say a family, F , of subsets of an n-set is weakly union-free i...
AbstractWe present a conjecture, with some supporting results, concerning the maximum size of a fami...
AbstractA union-closed family F is a finite collection of sets not all empty, such that any union of...
A family of sets is union-closed if it contains the union of any two of its elements. Reimer (2003) ...
AbstractA family of nonempty sets has the equal union property if there exist two nonempty disjoint ...
Given a set S of n integers, the problem is to decide whether there exist two disjoint nonempty subs...
AbstractA union closed familyAis a finite family of sets such that the union of any two sets inAis a...
AbstractA family F of k-subsets of an n-set X is disjoint union-free (DUF) if all disjoint pairs of ...
AbstractWe consider the maximal size of families of k-element subsets of an n element set [n] that s...
AbstractGiven k finite sets S1,…,Sk, to what extent is it possible to partition their union into two...
International audienceWe consider the problem of minimizing the size of a family of sets G such that...
An old problem of Moser asks: what is the size of the largest union-free subfamily that one can guar...
Given a family F of subsets of [n], we say two sets A,B ∈ F are comparable if A ⊂ B or B ⊂ A. Sperne...
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