Counting primitive subsets and other statistics of the divisor graph of $\{1,2, \ldots n\}$
Abstract
Let $Q(n)$ denote the count of the primitive subsets of the integers $\{1,2\ldots n\}$. We give a new proof that $Q(n) = \alpha^{(1+o(1))n}$ which allows us to give a good error term and to improve upon the lower bound for the value of this constant $\alpha$. 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, geometricprogressionfree sets, and the divisor graph pathcover problem.
 Publication:

arXiv eprints
 Pub Date:
 August 2018
 arXiv:
 arXiv:1808.04923
 Bibcode:
 2018arXiv180804923M
 Keywords:

 Mathematics  Number Theory;
 Mathematics  Combinatorics
 EPrint:
 22 pages. Significantly updated proof improves error terms. Improved bounds on numerical constants