1
vote
1answer
29 views

Coloring a binary tree

Working through a problems practice coloring, I have found a problem that has me stumped. The problem states: For $n \in \mathbb{R}_{>o}$ the binary tree is defined recursively as follows. The ...
0
votes
2answers
113 views

fill-in-the-blank induction proof

I'm stuck at homework task I'm working on. I would really appreciate some help. Here is the task: Let $f$ be a function on binary numbers defined recursively as follows. $f(0) = 1$ and ...
1
vote
0answers
135 views

1s surpassing 0s in binary strings of odd length

Let $A(k)$ be the number of distinct binary strings of length $2k+1,$ for which the number of $1$s surpasses the number of $0$s for the first time at digit number $2k +1$, i.e., in the final digit in ...