%0 Journal Article
%T Maximal independent sets and separating covers
%A Vincent Vatter
%J Mathematics
%D 2009
%I arXiv
%X In 1973, Katona raised the problem of determining the maximum number of subsets in a separating cover on n elements. The answer to Katona's question turns out to be the inverse to the answer to a much simpler question: what is the largest integer which is the product of positive integers with sum n? We give a combinatorial explanation for this relationship, via Moon and Moser's answer to a question of Erdos: how many maximal independent sets can a graph on n vertices have? We conclude by showing how Moon and Moser's solution also sheds light on a problem of Mahler and Popken's about the complexity of integers.
%U http://arxiv.org/abs/0911.4204v2