Yesterday I was asked about a problem coming from stringology. The problem was to prove something basic about strings. However, i am not a good mathematician as i ought to be so i am turning to you :). The problem was:
Let be a string such that is its i-th letter and the alphabet.
Theorem: Given S, a substring of length 1 starting at position i is either a unique or repeated.
so the problem is that i should show that any encountered letter is repeated somewhere else in the string or it occurs only once. However i don't know where to start. Also i am not quite sure if this is well-defined at all. At first i thought this looks like the case where i can prove that every number element of natural numbers is either odd or even but there is no such regularity as with natural numbers. so i am wondering is there a way to prove this or not. what necessary additional information is required to prove this statement? Does anyone know about any similar cases ?