| Autor: |
Hao, Steven, He, Andrew, Li, Ray, Wu, Scott |
| Rok vydání: |
2014 |
| Předmět: |
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| Druh dokumentu: |
Working Paper |
| Popis: |
Cayley's formula states that the number of labelled trees on $n$ vertices is $n^{n-2}$, and many of the current proofs involve complex structures or rigorous computation. We present a bijective proof of the formula by providing an elementary calculation of the probability that a cycle occurs in a random map from an $n$-element set to an $n+1$-element set. |
| Databáze: |
arXiv |
| Externí odkaz: |
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