Abstract
In 1991 Renaud defined a boundary function φ(n) for union-closed sets, and evaluated it to n = 17. Also in 1991, Mallows examined a sequence a(n) defined recursively by Conway in 1988.Investigation of some properties of strictly reduced ordered power sets, a class of union-closed sets, leads to the conclusion that a(n + 1) is an upper bound for φ(n), and the union-closed sets conjecture holds if the conjecture φ(n) = a(n + 1) is valid.
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