A Cameron and Erdős Conjecture on Counting Primitive Sets
A Cameron and Erdős Conjecture on Counting Primitive Sets
复制标题
卡梅伦和埃尔多斯关于计算原始集的猜想
作者：
Rodrigo Angelo
让$f（n）$计数${1，..}的子集的数量，n}$没有一个元素分割另一个元素。在本文中，我证明了f（n）的增长类似于某个真实的数的n次幂，在这个意义上，lim_{n
存在ightarrow infty}f（n）^{1/n}$。这证实了一个猜想的卡梅隆和埃尔德“os，提出了一份文件，他们研究了一些类似的问题，包括著名的“卡梅隆-埃尔德“os os猜想”计数和自由子集。
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 $lim_{n
ightarrow infty}f(n)^{1/n}$ exists. This confirms a conjecture of Cameron and Erd"os, proposed in a paper where they studied a number of similar problems, including the well known "Cameron-Erd"os os Conjecture" on counting sum-free subsets.