High Quality Content by WIKIPEDIA articles! 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 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. Distinct numbers correspond to distinct k-combinations, and produce them in lexicographic order; moreover 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. Данное издание...

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