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# Permutations

#### Check

Checks whether an array represents a permutation.
 bool check (int n, int *p)

#### Ascending Subsequence

Finds the longest ascending subsequence of a permutation.
 std::vector ascending_subsequence (int n, int *a)

#### Breaks

Counts the number of breaks in a permutation.
 int break_count (int n, int *p)

#### Cycles

Counts the number of cycles in a permutation.
 int cycles (int n, int *p)

#### Derangement Check

Verifies if a given permutation is a derangement.
 bool derangement_check (int n, int *a)[inline]

#### Inverse

Calculates the inverse of the given permutation.
 std::vector inverse (int n, int *p)

#### Inverse Large

Calculates the inverse of the given permutation.
 std::vector inverse_large (int n, int *p)

#### Inversion Sequence

Computes the inversion sequence of a permutation.
 std::vector inversion_sequence (int n, int *p)

#### Multiplication

Computes the product of two permutations.
 std::vector multiplication (int n, int *p1, int *p2)

#### Partition

Computes the partition generated by the given permutation.
 std::vector partition (int n, int *p)

#### Rank

Computes the rank of the given permutation, as generated by Permutation Class 2.
 int rank (int n, int *p)

#### Sign

Calculates the sign of the given permutation.
 int sign (int n, int *p)

#### Ulam Distance

Computes the Ulam metric distance of two permutations.
 int ulam_distance (int n, int *a, int *b)[inline]

#### Unrank

Returns the permutation of the given rank, as generated by the Permutation Class 2 component.
 std::vector unrank unknown (int n, int rank)

#### Unused Items

Reports the unused items in a partial permutation.
 std::vector unused_items unknown (int n, int npart, int *part)

#### Permutation1

Progressively generates all the permutations of the given size.

#### Permutation2

Progressively generates all the permutations of the given size.

#### Permutation3

Progressively generates all the permutations of the given size.

#### Permutation Lex

Progressively generates all the permutations of the given size, in lexicographic order.