Description
Abstract: In the first half-hour, Petar Marković will present the Equivalence Theorem, a 2004 result by V. Božin from his PhD thesis (never published in a journal). In a probability theory-inspired approach, he proved an equivalent condition to Frankl's Union-Closed Sets Conjecture. Ths equivalent condition is chiefly useful if one hopes to construct a counterexample to Frankl's conjecture, since each counterexample to Frankl's conjecture is trivially a counterexample to the equivalent. On the other hand, starting from a counterexample to the equivalent, a complicated construction produces a huge counterexample to Frankl's Conjecture. We will state the theorem, outline the structure of its proof and some constructions used in that proof. In the final third of the lecture, Vladimir Božin will show some ideas which may be useful in constructing a counterexample to the equivalent condition.