A new generic class of Frankl’s families

Frankl’s conjecture states that in a family of sets closed by union F such that F 6= {∅}, there is an element that belongs to at least half of the sets of F. There are several partial results of this conjecture. For example, it has been shown that families in which the smallest set is of size 1 or 2, or families closed both by union and by intersection are Frankl’s. In this article, by basing ourselves on an unseen recursive definition of the family of sets closed by union, we will define a new class of Frankl’s families. Subsequently, we will evaluate the size of this class for the first 6 values of n. Finally we will show that this class does not coincide with the already known Frankl’s classes