I want to describe the relationship between largest word length, l, and the number of words in a set, n.
Example:
- For the set of words
{"the", "large", "rock"}, the largest word length is l = 5 - For
{"ten", "two", "cat"}, the largest word length is l = 3 - For
{"a", "Mathematics"}, the largest word length is l = 11
Can l be approximated as a function of n? How is l related to n?
If n were allowed to be very large, l would obviously be the length of the largest word in the English language. If n were limited to 1, l would obviously be the average size of all words. Intuition tells me that choosing more words gives me a statistically better chance of requiring a more buckets, but I can't explain why.
I am not sure whether this question belongs on StackOverflow or Mathematics. This is not a homework problem. It came up in an answer I posted over on StackOverflow.