Counting forests

Lajos Takács
1990 Discrete Mathematics  
In 1889 A. Cayley stated that the number of forests with n labeled vertices that consist of s distinct trees such that s specified vertices belong to distinct trees is snn-'-' for 1 <s c n. In this paper Cayley's formula is proved in a simple and elementary way.
doi:10.1016/0012-365x(90)90139-9 fatcat:qa5vwusmvbgr3l2jjyyuhissp4