Generalized symmetric group
= Generalized symmetric group
{wiki=Generalized_symmetric_group}
The generalized symmetric group, usually denoted \\( \\text\{GS\}(n, k) \\) or \\( S(n, k) \\), is a mathematical concept that generalizes the classical symmetric group, which consists of all permutations of a finite set. Specifically, the generalized symmetric group relates to the permutations and possible arrangements of \\( n \\) objects taken \\( k \\) at a time. \#\#\# Definition 1.