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A remark on the enumeration of rooted labeled trees

Sokal, AD; (2020) A remark on the enumeration of rooted labeled trees. Discrete Mathematics , 343 (7) , Article 111865. 10.1016/j.disc.2020.111865. Green open access

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Abstract

Two decades ago, Chauve, Dulucq and Guibert showed that the number of rooted trees on the vertex set [n+ 1] in which exactly k children of the root are lower-numbered than the root is n k � n n−k . Here I give a simpler proof of this result.

Type: Article
Title: A remark on the enumeration of rooted labeled trees
Open access status: An open access version is available from UCL Discovery
DOI: 10.1016/j.disc.2020.111865
Publisher version: https://doi.org/10.1016/j.disc.2020.111865
Language: English
Additional information: This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.
Keywords: Trees, rooted trees, labeled trees, enumeration, Chu–Vandermonde identity, Abel identity
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics
URI: https://discovery.ucl.ac.uk/id/eprint/10092117
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