In mathematics, a combinadic is an ordered integer partition, or composition. Combinadics provide a lexicographical index for combinations. Applications for combinadics include software testing, sampling, quality control, and the analysis of gambling games such as Canada's national 6/49 lottery. For definiteness, we will consider the k-combinations on the set S = {0, 1, ..., n ? 1} of the first n integers starting from 0. Recall that there are C(n,k) = n! / ( k! (n ? k)! ) of these. The index we are looking for is the mapping associating the numbers i = 0, 1, ..., C(n,k) ? 1 with the list of k-combinations having their elements written in ascending order, and themselves ordered lexicographically. By abuse of notation we denote as C(n,k)(i) the ith k-combination taken from the set of n elements. Then the index for the ten 3-combinations of the set of five elements {0, 1, 2, 3, 4} can be written out as follows.

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