Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, and in particular in combinatorics, the combinatorial number system of degree k, also referred to as combinadics, is a correspondence between natural numbers N and k-combinations, represented as strictly decreasing sequences ck < ... < c2 < c1 ≥ 0. Since the latter are strings of numbers, one can view this as a kind of numeral system for representing N, although the main utility is representing a k-combination by N rather than the other way around. 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.