Thumbnail
Access Restriction
Open

Author Vatter, Vincent
Source arXiv.org
Content type Text
File Format PDF
Date of Submission 2009-11-21
Language English
Subject Domain (in DDC) Natural sciences & mathematics ♦ Mathematics
Subject Keyword Mathematics - Combinatorics ♦ math
Abstract 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.
Educational Use Research
Learning Resource Type Article


Open content in new tab

   Open content in new tab