What design pattern to use for instantited objects containing permutations of a string?

I would like to know if there is a design pattern to cover making multiple objects representing mutiple permutations of a string. For example:

I have a database table containing item names. Each item has a sort of "signature" (can't think of a better word for it), which is all the letters of the item name, sorted in alphabetical order with the spaces removed.

Given a "soup string" of jumbled up letters, I would like to sort those letters in alphabetical order to match it to a signature in the database, but here's the catch...

Each soup string may contain a few extra letters. So what I'm looking for is a design pattern which would be suitable for taking a string and returning a list of objects, each representing a permutation of that soup string, which I can then fire at the database.

I was thinking about just using a factory, but isn't this outside of the scope of a factory? It does contain logic, (am I right in saying this is not business logic?), but perhaps this is acceptable for a factory or factory method? Then again, perhaps this is an perfect usecase for a factory.

Ultimately, I will probably just go with the factory method. I just wanted to see if there was a better option.

Thanks in advance.