Library/Combinatorics/Classical combinatorics/Permutations and substitutions/Permutations and substitutions (other)

Permutations and substitutions (other)

Overview
Important

Beyond basic permutations (arrangements of objects), there are many interesting variations and extensions. These include: permutations with restrictions (such as fixing or forbidding certain positions), circular permutations (arranging objects in a circle), and permutations with repeated elements (multisets). Studying these helps solve more complex counting problems.

Important properties

  • Permutations with restrictions: Sometimes, certain objects must or must not be in specific positions.

  • Circular permutations: Arrangements where rotations are considered the same (e.g., seating people around a round table).

  • Permutations of multisets: Counting arrangements when some objects are identical.

  • Derangements: Permutations where no object appears in its original position.