Counting primitive subsets and other statistics of the divisor graph of \1,2, … n\

2018/08/14 by Nathan McNew, McNew, Nathan · 1 citation
Mathematics · #Analytic Number Theory Research #Limits and Structures in Graph Theory #Advanced Mathematical Identities

paper · pdf · doi:10.48550/arxiv.1808.04923

Abstract

Let Q(n) denote the count of the primitive subsets of the integers \1,2… n\. We give a new proof that Q(n) = α^(1+o(1))n which allows us to give a good error term and to improve upon the lower bound for the value of this constant α. We also show that the method developed can be applied to many similar problems that can be stated in terms of the divisor graph, including other questions about primitive sets, geometric-progression-free sets, and the divisor graph path-cover problem.

Citations

• On large primitive subsets of \1,2,…,2n\

Cited by

• On divisibility relation graphs

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