# What does it mean when someone say “as long as a value (say x) is linear in another value (say n)”?

I was reading about bucket sort and then I came to the following statement:

"As long as the input has the property that the sum of the squares of the bucket sizes is linear in total number of elements ..."

What does it actually mean? Suppose total number of elements is $10$. Then what set of numbers satisfy the statement, "$x$ is linear in $10$."

• I don't think it would make much sense to most readers to say that a given variable $x$ is linear in some constant (say, $10$). There's no generally understood sense in which a variable can be said to be directly proportional to a constant. So I don't think I would say that you were wrong so much as I would say I don't really understand what you mean. – Brian Tung Sep 3 '15 at 6:41