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?