Linked from

The 48 pages that link to Permutation, each with the reason it gives.

• Group actionRelated: Each group element acts as a permutation of the underlying set.

• FactorialRelated: The n! permutations of n distinct objects count every possible ordering.

• GroupRelated: Permutations compose associatively, have an identity, and can be undone.

• Fermat's little theoremRelated: Multiplication by a permutes the nonzero residues modulo p, yielding a product-based proof.

• Orbit-stabilizer theoremRelated: Each group element acts as a permutation of the set.

• Sorting algorithmRelated: A correct sort changes element order without losing or duplicating elements.

• Falling factorialRelated: The falling factorial counts ordered selections of n distinct objects from x choices.

• MajorizationRelated: Majorization ignores the original order of entries by sorting or permuting vectors.

• Sol LeWittRelated: Permutation systems generate many distinct arrangements from a limited set of forms.

• Wilson's theoremRelated: Multiplication by a nonzero residue permutes the nonzero residues modulo a prime.

• Dilworth's theoremRelated: Order comparisons among permutation entries yield chain and antichain decompositions.

• Riemann series theoremRelated: A rearrangement must reorder every term without omitting or duplicating any.

• Block cipherRelated: For a fixed key, a block cipher maps every possible input block to a unique output block.

• Discrete uniform distributionRelated: Uniform sampling over permutations models a randomly chosen ordering of finite outcomes.

• Binet–Cauchy identityRelated: Determinants encode signs of permutations, which govern signs in minor expansions.

• Cauchy–Binet formulaRelated: Determinant expansions over permutations underlie the formula's signs and terms.

• Georges PerecRelated: Permutations and combinatorial structures informed Perec’s methods for generating literary forms.

• Muirhead's inequalityRelated: The symmetric sum is formed by permuting the exponents among the variables.

• Travelling salesman problemRelated: Candidate tours can be represented as city orderings, though many orderings describe the same cycle.

• Bertrand's ballot theoremRelated: A random ballot is a permutation of the votes, with votes of the same candidate treated as indistinguishable.

• Mutually orthogonal Latin squaresRelated: Every row and column of a Latin square is a permutation of its symbols.

• Algebraic combinatoricsRelated: Permutations are fundamental objects studied through algebra, statistics, and enumeration.

• Combinatorial principlesRelated: The product rule counts the successive positions in an arrangement.

• Lah numberRelated: Concatenating the lists gives a permutation, with cuts marking the blocks.

• Lévy–Steinitz theoremRelated: Rearranging a series means applying a permutation to its term indices.