What is the maximum number of the distinct subwords of the word
AXIOMATIZABLE?
The answer is 88. But how?
What is the maximum number of the distinct subwords of the word
AXIOMATIZABLE?
The answer is 88. But how?
If I am counting right (this is the weak part of the argument!), our word has $13$ letters. If all the letters were different, there would be $1$ subword of length $13$, $2$ of length $12$, and so on up to $13$ of length $1$, for a total of $1+2+\cdots +13$. By the usual formula, or by addition, this sum is $91$.
However, there are some repeated subwords, all of length $1$, three A's and two I's. So we should subtract $2$ for the extra A's, and $1$ for the extra I. The result is indeed $88$.
Remark: A subword of the word $W$ is a string of letters that are consecutive in $W$. Permuting is not allowed.
Being a mathematician, I think that there are $89$ distinct subwords. This is because I count the empty word as a word; shouldn't everybody?