Definition:Prüfer Sequence
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Definition
A Prüfer sequence of order $n$ is a (finite) sequence of integers:
- $\left({\mathbf a_1, \mathbf a_2, \ldots, \mathbf a_{n-2}}\right)$
such that $\forall i: 1 \le i \le n-2: 1 \le \mathbf a_i \le n$.
That is, it is a (finite) sequence of $n - 2$ integers between $1$ and $n$.
Also known as
A Prüfer sequence is also known as a Prüfer code.
Historical note
The concept was originally defined for the purposes of demonstrating a proof of Cayley's Formula.
Source of Name
This entry was named for Heinz Prüfer.