The Moebius function of $P$ is a function defined at pairs of vertices of $P$ with the properties: $mu(a,a) = 1$ for all $a$ in $P$, and $mu(a,b) = -sum(mu(a,c))$ over all $a \leq c < b$.
The Moebius function of the $n$ chain is $1$ at $(a,a)$ for all $a$, $-1$ at $(a, a+1)$ for $1 \leq a < n$, and $0$ every where else.
i1 : moebiusFunction chain 3
o1 = HashTable{(1, 1) => 1 }
(1, 2) => -1
(1, 3) => 0
(2, 1) => 0
(2, 2) => 1
(2, 3) => -1
(3, 1) => 0
(3, 2) => 0
(3, 3) => 1
o1 : HashTable
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The object moebiusFunction is a method function.