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Maths › Combinatorics ›

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<int> 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<int> inverse (int n, int *p)

Inverse Large

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

Inversion Sequence

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

Multiplication

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

Partition

Computes the partition generated by the given permutation.
std::vector<int> 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<int> unrank unknown (int n, int rank)

Unused Items

Reports the unused items in a partial permutation.
std::vector<int> 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.