C++ :: Sequentially Remove One Element From Vector At A Time With Replacement?

I have a vector of int,

Code:
vector<int> row_numbers{1,2,3,4,5,6,7,8,9};

I want to sequentially remove one element at a time starting with the first. When the second element is removed, the first element needs to go back in. The sequence would look like

Code:
// original vector, row_numbers.size()=9
row_numbers{1,2,3,4,5,6,7,8,9};
// trimmed vector, row_numbers_trim.size()=8

[Code] .......

I have been working under the assumption that the best method would be to have row_numbers remain untouched and work on a copy. For each step in the sequence, you would create row_numbers_trim as a copy of row_numbers, and then remove an element from row_numbers_trim.

Code:
// position being removed
int counter = 0;
// copy original vector
row_numbers_trim = row_numbers;
// remove the first element from the copy
row_numbers_trim(row_numbers_trim.begin()+counter);

All you would have to do here is to increment counter in a loop. is there a better way?