NumberOfPermutationsByInversions[n, k] gives the number of permutations of length n with exactly k inversions. NumberOfPermutationsByInversions[n] gives a table of the number ...

OddGraph[n] returns the graph whose vertices are the size-(n - 1) subsets of a size-(2 nTraditionalForm\`\[Dash]1) set and whose edges connect pairs of vertices that ...

ParentsToPaths[l, i, j] takes a list of parents l and returns the path from i to j encoded in the parent list. ParentsToPaths[l, i] returns the paths from i to all vertices.

PartitionQ[p] yields True if p is an integer partition. PartitionQ[n, p] yields True if p is a partition of n.

PermuteSubgraph[g, p] permutes the vertices of a subgraph of g induced by p according to p.

RandomSubset[l] creates a random subset of set l.

RGFToSetPartition[rgf, set] converts the restricted growth function rgf into the corresponding set partition of set.

SetPartitions[set] returns the list of set partitions of set. SetPartitions[n] returns the list of set partitions of {1, 2, ..., n}.

SetPartitionToRGF[sp, set] converts the set partition sp of set into the corresponding restricted growth function.

Strings[l, n] constructs all possible combinatorial strings of length n from the elements of list l.