# Hasse Diagrams of Integer Divisors

Hasse Diagrams of Integer Divisors

A Hasse diagram is a graphical representation of a partially ordered set (poset). The set consisting of the divisors of a positive integer can be considered a poset under the relation if divides . For this poset, any edge in the diagram is such that the number below divides the number immediately above. If is a product of prime numbers, then is isomorphic to the set of subsets of with the relation if is contained in ; hence, is a Boolean algebra in this case.

D(n)

n

a≺b

a

b

n

k

D(n)

{1,2,...,k}

a≺b

a

b

D(n)