In mathematics, and in particular in combinatorics, the combinatorial number system of degree "k" (for some positive integer "k"), also referred to as combinadics, is a correspondence between natural numbers (taken to include 0) "N" and "k"-combinations, represented as strictly decreasing sequences "c""k" > ... > "c"2 > "c"1 ≥ 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. Distinct numbers correspond to distinct "k"-combinations, and produce them in lexicographic order; moreover the numbers less than formula_1 correspond to all "k"-combinations of }. 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.