What is the mathematical expression of ascending sort?

Can you be more explicit about what you're asking? I'm sure it makes sense to you, but I don't know what you're trying to say, and I'm sure I'm not alone.

For reference, I have a PhD in pure math, and I've done research in sorting algorithms and their performance, so I might be able to answer your question, if only I knew what it was ...

Mathematically you could express the concept of a (partially ordered) set by something like <S,P(x1,x2)> (where P is some comparison function), so, for example, the sorted natural numbers would be <N,<>. I have no idea, though, if that's even remotely close to what you're asking.