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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.

Ancestors (6)

  1. Permutation groups
  2. Permutations
  3. Combinatorics
  4. Fields of mathematics
  5. Mathematics
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