what's the name for asymptotic without multiplier?

(In combinatorics) When talking about asymptotic behaviour of a function. Seemingly we have already decided the multiplier. For example, we would say $$\binom{n}{2}$$ is asymptotically $$1/2*n^2$$, but not $$n^2$$. My question is, what should we say about a function $$f$$ if we only know $$\lim \frac{f}{n^2}$$ is bounded away from $$0$$ and $$\infty$$, but don't know that exact number?

• You're looking for "big Theta" notation. – Antonio Vargas Sep 25 '18 at 9:43

It's a notation that "ignores the constant factor". By definition, $$f\in O(g)$$ if there exists some constant $$C$$ such that $$f(x) for all large enough values of $$x$$. For example, $$an^2+bn+c\in O(n^2)$$ no matter what the particular constants $$a,b,c$$ are.