============================================================
   Seminário de Teoria da Computação e Combinatória (TCC)

  Manhã de Combinatória Extremal e Métodos Probabilísticos
============================================================

Título:      A refinement of the Cameron-Erdos Conjecture
            
Palestrante: Robert David Morris
             Instituto de Matemática Pura e Aplicada

Hora e Data: 11h35m, quarta-feira, 31 de outubro de 2012

Local:       Sala Multi-usos do Numec

Resumo:

A set of integers  (or a subset of a group G)  is said to be
sum-free if it contains no solution  to the equation x + y =
z$.   In 1990,  Cameron and  Erd\H{o}s conjectured  that the
number of  sum-free subsets of  the set \{1, \ldots,  n\} is
O(2^n), within a constant  factor of the trivial lower bound
(consider subsets of the odds). The conjecture was proven in
2004 by Green, and independently by Sapozhenko. 

In  this talk,  I  shall  explain how  to  prove a  `sparse'
version of the Cameron-Erd\H{o}s Conjecture, by giving close
to best possible bounds on the number of sum-free subsets of
\{1, \ldots, n\} of size m, for every 1 \leq m \leq n.

This  is  joint  work  with  Noga Alon,  József  Balogh  and
Wojciech Samotij.