Kelement

Kelement is a term used informally in mathematics and computer science to refer to either a k-element subset of a finite set or the k-th element in a sequence. It is not a standardized formal term, and its precise meaning depends on context.

In combinatorics, a kelement subset of a finite set S with cardinality n is any subset containing exactly k elements, where 0 ≤ k ≤ n. The number of kelement subsets is given by the binomial coefficient C(n, k). This concept underpins many counting problems such as selecting committees, groups, or samples. While the standard phrasing is “k-element subset,” some texts shorten it to kelement for brevity.

In sequences and arrays, a kelement may refer to the element at position k, i.e., the k-th element. This usage depends on indexing conventions; some authors adopt 1-based indexing (the first element is position 1), while others use 0-based indexing (the first element is position 0).

Example: Let S = {1, 2, 3, 4} and k = 2. The 2-element kelements are the subsets {1,2}, {1,3}, {1,4}, {2,3}, {2,4}, and {3,4}. In a sequence a1, a2, a3, a4, the 3rd kelement is a3.

See also: k-element subset, binomial coefficient, k-th element, indexing.