# Tagged Questions

**2**

votes

**1**answer

219 views

### A variant of Kruskal's theorem

For $X$ and $Y$ finite sequences of finite trees, let us say that $X$ is everywhere contained in $Y$ ($X\subseteq_{ec}Y$) iff, for every $y\in Y$, there is some $x\in X$ such that $x$ is a minor of ...

**0**

votes

**0**answers

85 views

### Database of non-isomorphic trees

As there are several free prime number databases, is there something similar for non-isomorphic trees?

**2**

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**0**answers

34 views

### Finding the number of leaf nodes at specific level of a random tree

Given a uniform recursive tree (URT) of size $N$ rooted at one node whereby the tree is generated as follows:
Starting with a root node, at each iteration, a new node is connected to one of the ...

**2**

votes

**1**answer

169 views

### More asymptotics for trees

This is a follow up to my recent question on the asymptotics of A003238. Lucia gave a fine answer to that question, but as I hinted the 'real' problem I have in mind is slightly different, and I've ...

**5**

votes

**2**answers

175 views

### Average number of distinguished leaves in a binary tree

By a binary tree, I mean in this question a full rooted binary tree in which left and right child are labeled. A leaf of such a tree is a vertex of degree at most 1 (most references would probably ...

**13**

votes

**1**answer

376 views

### Are the asymptotics of A003238 known?

Sequence A003238 of the OEIS counts ``rooted trees with $n$ vertices in which vertices at the same level have the same degree.'' The sequence, $a$, begins
1, 1, 2, 3, 5, 6, 10, 11, 16, ...
and it is ...

**2**

votes

**0**answers

316 views

### Matula-Goebel ordering of rooted trees intrinsic?

I was somewhat recently introduced to the Matula-Goebel bijection between rooted trees and natural numbers. (nicely illustrated here http://keithbriggs.info/matula.html) Looking through them, I ...

**9**

votes

**2**answers

423 views

### Series defined by a fixed-point functional equation

Description
I my work, I met fixed-point functional equations of a very specific form. Since I am not expert in the domain of functional equations, I have not pushed the study of these very far. Here ...

**23**

votes

**9**answers

2k views

### Is the empty graph a tree?

This is a boring, technical question that I stumbled upon while making a contribution to Sage. I would still like to hear a constructive answer so hopefully the question does not get closed.
The ...

**5**

votes

**2**answers

240 views

### Number of trees with the same matching number

Let $\sigma(n,m)$ be the number of trees with $n$ vertices $\{ v_1, \dots, v_n \}$ such that the matching number (the size of a maximum matching) is $m$.
I have been trying to compute the value of ...

**3**

votes

**1**answer

191 views

### A distinguishing node property in trees?

Consider a tree with k nodes and for each node v the vector lv = (lv0, lv1, ..., lvk-1) with lvd the number of leaves (!) with distance d to v. I wonder whether two nodes v, w with lv = lw are ...