Abstract
We show that the Union-Closed Conjecture holds for the union-closed family generated by the cyclic translates of any fixed set.
Highlights
If X is a set, a family F of subsets of X is said to be union-closed if the union of any two sets in F is in F
We show that the Union-Closed Conjecture holds for the union-closed family generated by the cyclic translates of any fixed set
If X is a set and F is a family of subsets of X, we say F is transitive if the automorphism group of F acts transitively on X. (The automorphism group of F is the set of all permutations of X that preserve F.) Informally, F is transitive if all points of X ‘look the same’ with respect to F
Summary
If X is a set, a family F of subsets of X is said to be union-closed if the union of any two sets in F is in F. Mathematical Institute University of Oxford United Kingdom james.aaronson.maths@gmail.com We show that the Union-Closed Conjecture holds for the union-closed family generated by the cyclic translates of any fixed set.
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