$\ D_n = \sum_{i,j,k}^n ε_{ijk}···a_i b_j c_k ··· , $
where $\ ε_{ijk···} $, analogous to the Levi-Civita symbol of Section 2.9, is +1 for even permutations1 (ijk ···) of (123 ···n),−1 for odd permutations, and zero if any index is repeated.
This is from Arfken's Mathematical methods for Physicists 6th edition. Now I understand that 123 has 6 permutations. But what are odd and even permutations?!