| Abstract:
The well-known Frankl's Conjecture (FC) has been translated into many
different dialects of Discrete Mathematics including Lattice Theory. I
believe FC was originally given in terms of Union-Closed families of sets.
Arguably the most natural way to think about FC is via the `natural
representation of a finite lattice'. I will review this elementary
material. I will then introduce some natural notions of reducibility for
u.c-families and hence for finite lattices. I believe that
counting/characterizing irreducible u.c-families could shed light on FC
and, maybe, other things.
|
