Subsequently, it was discovered that the absolute values |"s"("n", "k")| of these numbers are equal to the number of permutations of certain kinds. These absolute values, which are known as unsigned Stirling numbers of the first kind, are often denoted formula_7 or formula_8. They may be defined directly to be the number of permutations of "n" elements with "k" disjoint cycles. For example, of the formula_9 permutations of three elements, there is one permutation with three cycles (the identity permutation, given in one-line notation by formula_10 or in cycle notation by formula_11), three permutations with two cycles (formula_12, formula_13, and formula_14) and two permutations with one cycle (formula_15 and formula_16). Thus, formula_17, formula_18 and formula_19. These can be seen to agree with the previous calculation of formula_20 for formula_21.