A remark on the enumeration of rooted labeled trees
| Autor: | Alan D. Sokal |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Discrete mathematics
Vertex (graph theory) 020206 networking & telecommunications 0102 computer and information sciences 02 engineering and technology 05A15 (Primary) 05A10 05A19 05C05 (Secondary) 01 natural sciences Theoretical Computer Science Combinatorics 010201 computation theory & mathematics FOS: Mathematics 0202 electrical engineering electronic engineering information engineering Enumeration Mathematics - Combinatorics Discrete Mathematics and Combinatorics Combinatorics (math.CO) Mathematics |
| Zdroj: | Discrete Mathematics. 343:111865 |
| ISSN: | 0012-365X |
| Popis: | 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 $\binom{n}{k} \, n^{n-k}$. Here I give a simpler proof of this result. LaTex2e, 9 pages. Version 2 contains a Note Added with a quick and elegant proof due to Jiang Zeng. To be published in Discrete Mathematics |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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