WOLFRAM|DEMONSTRATIONS PROJECT

Hasse Diagrams of Integer Divisors

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n
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A Hasse diagram is a graphical representation of a partially ordered set (poset). The set
D(n)
consisting of the divisors of a positive integer
n
can be considered a poset under the relation
a≺b
if
a
divides
b
. For this poset, any edge in the diagram is such that the number below divides the number immediately above. If
n
is a product of
k
prime numbers, then
D(n)
is isomorphic to the set of subsets of
{1,2,...,k}
with the relation
a≺b
if
a
​
is contained in
b
; hence,
D(n)
is a Boolean algebra in this case.