Petr's blog

A week with Cayley
By Petr, 9 years ago, In English

http://petr-mitrichev.blogspot.com/2015/02/this-week-in-competitive-programming_19.html

  • Vote: I like it
  • +38
  • Vote: I do not like it

Comments Comments (1)
| Write comment?
»
9 years ago, # |
  Vote: I like it 0 Vote: I do not like it

In fact there are many generalizations of Cayley theorem (though I didn't know that particular one).

One was given as a problem on Putnam competition one year ago: http://www.artofproblemsolving.com/Forum/viewtopic.php?p=3315688&sid=56608f6bc111f1ce8bcfb33ff1220ce3#p3315688

Here is another one I know. Assume that we want to compute number of forests on n vertices with k trees such that vertices with indiced 1, ..., n belong to other trees. Then number of them is equal to knn - k - 1.

Despite the fact that there are many of them I always got problems even with proving basic version :p.

→ Reply