In mathematics, and in particular in combinatorics, the combinatorial number system of degree k, also referred to as combinadics, or the Macaulay representation of an integer, is a correspondence between natural numbers N and k-combinations. The combinations are represented as strictly decreasing sequences ck > ... > c2 > c1 ≥ 0 where each ci corresponds to the index of a chosen element in a given k-combination. Distinct numbers correspond to distinct k-combinations, and produce them in lexicographic order. The numbers less than correspond to all k-combinations of {0, 1, ..., n − 1}. The correspondence does not depend on the size n of the set that the k-combinations are taken from, so it can be interpreted as a map from N to the k-combinations taken from N; in this view the correspondence is a bijection.