Given a permutation {p_1, p_2, ..., p_n} of {1, ..., n}, the bumping algorithm constructs a standard Young tableau by inserting the p_i one by one into an already constructed Young tableau. To apply the bumping algorithm, start with {{p_1}}, which is a Young tableau. If p_1 through p_k have already been inserted, then in order to insert p_(k + 1), start with the first line of the already constructed Young tableau and search for the first element of this line which is greater than p_(k + 1). If there is no such element, append p_(k + 1) to the first line and stop. If there is such an element (say, p_p), exchange p_p for p_(k + 1), search the second line using p_p, and so on.

tableau class | Young tableau