Lyndon word

Okay, so imagine you have a bunch of letters, like A, B, C, and so on. If you put them together in a certain order, you might make a word like CAT or DOG. But what if you wanted to make a really special kind of word that has a neat property?

That's where a Lyndon word comes in! A Lyndon word is a type of special word that has a couple of cool things about it.

Firstly, it's made of smaller "pieces" called Lyndon factors. These factors are like building blocks that you can shift around and rearrange to make lots of different Lyndon words.

Secondly, a Lyndon word is always in what's called "normal form", which means it's arranged in a very specific way. It starts with the smallest Lyndon factor, then the next smallest, and so on, all the way up to the largest.

Think of it like building a pyramid out of blocks, where each layer has one fewer block than the one below it. A Lyndon word is like that - it's made of building blocks that are arranged in a very specific order that makes it special.

So, in summary: a Lyndon word is a special kind of word that's made of building blocks called Lyndon factors, arranged in a particular order that makes it really neat!