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Posts Tagged ‘ combinatorics ’

29 December

Counting Binary Trees (The Hard Way)

In this post, we prove the closed form of a nonlinear recurrence corresponding to the count of binary trees with n nodes.

9 November
Posted in Article, Math Problems

Counting Words

Suppose that we are given the alphabet \Sigma = \Rec{0,1,2}; a word of length n: x_n \in \Sigma^5, is an ordered n-tuple whose elements all came from \Sigma. For example, a word of length 5 in \Sigma might be the tuple (0,0,2,1,0), which we will hereon denote as 00210. For some natural number k \le n, how many words of length n are there that contains exactly k zeros?