DIVISOR TOPOLOGIES AND THEIR ENUMERATION
نویسندگان
1 Department of Pure Mathematics, Ferdowsi University of Mashhad, P.O. Box 1159, Mashhad, Iran.
2 Department of Computer Science, School of Mathematics, Statistics and Computer Science, University of Tehran, P.O. Box 141556619, Tehran, Iran.
3 Department of Pure Mathematics, Ferdowsi University of Mashhad, P.O. Box 1159, Mashhad, Iran.
doi
10.22044/jas.2021.9712.1473چکیده
For a positive integer $m$, a subset of divisors of $m$ is called a \textit{divisor topology on $m$} if it contains $1 $ and $m$ and it is closed under taking $\gcd$ and $\rm lcm$. If $m=p_1\dots p_n$ is a square free positive integer, then a divisor topology $m$ corresponds to a topology on the set $[n]=\{1,2,\ldots,n\}$. Giving some facts about divisor topologies, we give a recursive formula for the number of divisor topologies on a positive integer.
