Some results and conjectures related to Frankl’s union closed conjecture
Rein van der Hout (Independent researcher)
Kees Roos (TU Delft - Discrete Mathematics and Optimization)
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Abstract
A union-closed family F is a finite collection of distinct subsets of a finite set such that the union of two subsets in F belongs to F . Péter Frankl conjectured in 1979 that, for any such family, there exists an element that belongs to at least half of its sets. This conjecture is still unsolved. In this paper, we present some results and conjectures related to Frankl’s conjecture. The new conjectures are based on evidence provided by some experimental results.
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