A note on Pr\"{u}fer--like coding and counting forests of uniform hypertrees

Abstract : This note presents an encoding and a decoding algorithms for a forest of (la- belled) rooted uniform hypertrees and hypercycles in linear time, by using as few as n − 2 integers in the range [1, n]. It is a simple extension of the classical Prüfer code for (labelled) rooted trees to an encoding for forests of (labelled) rooted uniform hypertrees and hypercycles, which allows to count them up according to their number of vertices, hyperedges and hypertrees. In passing, we also find Cayley's formula for the number of (labelled) rooted trees as well as its generalisation to the number of hypercycles found by Selivanov in the early 70's.
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Journal of Discrete Algorithms, Elsevier, 2012, 12 (1), 29--36 (selected paper of ACiD 2010)
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Christian Lavault. A note on Pr\"{u}fer--like coding and counting forests of uniform hypertrees. Journal of Discrete Algorithms, Elsevier, 2012, 12 (1), 29--36 (selected paper of ACiD 2010). 〈hal-00905902〉

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