Equation for the number of unlabeled trees on n vertices

  • Thread starter TheMathNoob
  • Start date
  • Tags
    Trees
In summary: Many years ago I wasted some time at another "easy" problem: the Collatz conjecture. It is so elementary in its statement that I thought it should be relatively easy to solve. There was a little voice in my head that warned me that brighter minds had tried it for decades, but still, I tried too. :oldsmile:I'm sorry to hear that. I hope you weren't discouraged by that experience. It's always nice to have a goal to strive for, even if it's something as small as this.
  • #1
TheMathNoob
189
4
Why has no one figured out yet an equation to count the number of unlabeled trees on n vertices?. I also have this dilemma between researchers and non-researchers. A researcher is just someone who is trying to find a solution to a problem for which no solution has been found yet. Right?, so if I try to find this equation, am I already doing research?
 
Physics news on Phys.org
  • #2
TheMathNoob said:
Why has no one figured out yet an equation to count the number of unlabeled trees on n vertices?. I also have this dilemma between researchers and non-researchers. A researcher is just someone who is trying to find a solution to a problem for which no solution has been found yet. Right?, so if I try to find this equation, am I already doing research?
No one has figured it out because it apparently is a difficult problem.
If you solve it, yes, that would qualify as research.

While I don't want to sound patronizing or discourage you to try it, in general a difficult open problem is, well, ..., difficult. Using your studying time efficiently is part of the art of studying.
But who knows? Maybe you have some novel idea to tackle the question that no one else thought of. It is possible, but a rare occurrence in the history of Mathematics.
 
  • #3
Samy_A said:
No one has figured it out because it apparently is a difficult problem.
If you solve it, yes, that would qualify as research.

While I don't want to sound patronizing or discourage you to try it, in general a difficult open problem is, well, ..., difficult. Using your studying time efficiently is part of the art of studying.
But who knows? Maybe you have some novel idea to tackle the question that no one else thought of. It is possible, but a rare occurrence in the history of Mathematics.
Yes, I understand what you are saying, but maybe it doesn't actually matter if I get to the solution or not. What matters is the knowledge and skills that I will acquire along the way. I also know that I still lack a lot of mathematical knowledge to give it a try, but maybe in the future XD. Why is it too hard?. It's just trees xd.
 
  • #4
TheMathNoob said:
Yes, I understand what you are saying, but maybe it doesn't actually matter if I get to the solution or not. What matters is the knowledge and skills that I will acquire along the way. Why is it too hard?. It's just trees xd.
Absolutely, try to tackle it for a (short) while if you like the problem, nothing wrong with that. At the very least it will give you some insight into why it is hard.

Many years ago I wasted some time at another "easy" problem: the Collatz conjecture. It is so elementary in its statement that I thought it should be relatively easy to solve. There was a little voice in my head that warned me that brighter minds had tried it for decades, but still, I tried too. :oldsmile:
 

1. What is the equation for the number of unlabeled trees on n vertices?

The equation for the number of unlabeled trees on n vertices is T(n) = (2n-3)!!, where !! represents the double factorial function.

2. How is this equation derived?

This equation is derived using the Cayley's formula, which states that the number of labeled trees on n vertices is equal to n^(n-2). Since there are n! ways to label a tree, the number of unlabeled trees is equal to n^(n-2) / n! = (2n-3)!!.

3. What is the significance of this equation?

This equation is significant because it provides a way to calculate the number of unlabeled trees on n vertices, which is useful in various fields such as graph theory, computer science, and biology. It also helps in understanding the complexity of problems related to trees.

4. Can this equation be used for any value of n?

Yes, this equation can be used for any positive integer value of n. However, for very large values of n, the resulting number may be too large to compute or represent accurately.

5. Are there any other ways to calculate the number of unlabeled trees on n vertices?

Yes, there are other methods such as using Prüfer sequences or Cayley's formula with Burnside's lemma. However, the equation T(n) = (2n-3)!! is the most commonly used and efficient method for calculating the number of unlabeled trees on n vertices.

Similar threads

  • Precalculus Mathematics Homework Help
Replies
12
Views
3K
  • Engineering and Comp Sci Homework Help
Replies
11
Views
1K
Replies
20
Views
2K
  • Set Theory, Logic, Probability, Statistics
Replies
7
Views
1K
  • Set Theory, Logic, Probability, Statistics
Replies
7
Views
2K
  • Set Theory, Logic, Probability, Statistics
Replies
2
Views
1K
  • Set Theory, Logic, Probability, Statistics
Replies
12
Views
968
  • Set Theory, Logic, Probability, Statistics
Replies
3
Views
1K
  • Engineering and Comp Sci Homework Help
Replies
1
Views
2K
  • Engineering and Comp Sci Homework Help
Replies
3
Views
2K
Back
Top