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Questions tagged [binary-tree]

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6
votes
0answers
64 views

Distributions of “sequential” binomials

I have come across the following stochastic process which seems very elementary, although I do not know any appropriate terminology for it; I greatly appreciate any suggestions! Suppose I am given ...
7
votes
1answer
248 views

Counting some binary trees with lots of extra stucture

While working on some computations on Hilbert schemes, I came across the following combinatorial problem. Let $D(k,n)$ be the weighted number of binary trees (children are left/right) with $n$ ...
5
votes
0answers
130 views

Rabin's proofs of emptiness and complementation problems for automata on infinite trees

I have originally asked this question on Math.SE, but I think it is more suitable here. I have been reading M. Rabin's 1969 article Decidability of Second-Order Theories and Automata on Infinite ...
1
vote
1answer
266 views

Ratio between number of nodes and leaves in a rooted binary tree

I want to know if there exists a positive constant $c$ such that: Given rooted binary tree, $T$, with root $r$ and height $h$ (not necessarily a full tree), the following holds: $$\frac{[\sum_{v \in ...
9
votes
0answers
278 views

Weighted sum of the Simsun (Andre) permutations

Let $ c_{n,k} $ be the Simsun permutations$^1$ defined by the following relations: $\displaystyle c_{n,0} = 1, \hspace{0.1cm} (n \ge 1);$ $$ c_{n,k} = (k+1) c_{n-1,k} +(n-2k+1) c_{n-1,k-1}, \hspace{0....
2
votes
2answers
204 views

Removing subtrees

Let $T$ be a complete infinite rooted binary tree. Is it possible to remove (infinitely many) subtrees of $T$ and get a subgraph $G$ such that: $G$ has no complete subtrees (the graph below any ...
10
votes
3answers
749 views

Combinatorial interpretation of composition of power series?

This is a minor curiosity that came up in a joint project recently. Consider the sequence $a_n=3\frac {(2n)!}{(n+2)!(n-1)!}$ (A000245 in OEIS). It has multiple combinatorial descriptions. One can ...
14
votes
0answers
367 views

Monotone embedding of complete binary tree in hypercube

Embedding different graphs, especially binary trees, in the hypercube has a huge literature. However, I could not find anything if we restrict the embedding to be monotone. So I would like to ...