A Cameron and Erdös conjecture on counting primitive sets

2017/11/22 by Rodrigo Angelo, Angelo, Rodrigo · 2 citations
Mathematics · #Limits and Structures in Graph Theory #Mathematical Dynamics and Fractals #Advanced Topology and Set Theory

paper · pdf · doi:10.48550/arxiv.1711.08107

Abstract

Let f(n) count the number of subsets of \1,...,n\ without an element dividing another. In this paper I show that f(n) grows like the n-th power of some real number, in the sense that lim_{n→ ∞}f(n)^1/n exists. This confirms a conjecture of Cameron and Erdös, proposed in a paper where they studied a number of similar problems, including the well known "Cameron-Erdös os Conjecture" on counting sum-free subsets.

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