2015/10/31 by Andy Loo, Loo, Andy
Mathematics · Engineering · Computer Science · #Limits and Structures in Graph Theory #graph theory and CDMA systems #Advanced Graph Theory Research
paper · pdf · doi:10.48550/arxiv.1511.00170
This paper discusses the question of how many non-empty subsets of the set [n] = \ 1, 2, ..., n\ we can choose so that no chosen subset is the union of some other chosen subsets. Let M(n) be the maximum number of subsets we can choose. We construct a series of such families, which leads to lower bounds on M(n). We also give upper bounds on M(n). Finally, we propose several conjectures on the tightness of our lower bound for M(n).