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

Partitions[n] constructs all partitions of integer n in reverse lexicographic order. Partitions[n, k] constructs all partitions of the integer n with maximum part at most k, ...

PerfectQ[g] yields True if g is a perfect graph, meaning that for every induced subgraph of g the size of a largest clique equals the chromatic number.

PermutationWithCycle[n, {i, j, ...}] gives a size-n permutation in which {i, j, ...} is a cycle and all other elements are fixed points.

PetersenGraph returns the Petersen graph, a graph whose vertices can be viewed as the size-2 subsets of a size-5 set with edges connecting disjoint subsets.

RadialEmbedding[g, v] constructs a radial embedding of the graph g in which vertices are placed on concentric circles around v depending on their distance from v. ...

RandomKSetPartition[set, k] returns a random set partition of set with k blocks. RandomKSetPartition[n, k] returns a random set partition of the first n natural numbers into ...

RandomSetPartition[set] returns a random set partition of set. RandomSetPartition[n] returns a random set partition of the first n natural numbers.

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

RankBinarySubset[l, s] gives the rank of subset s of set l in the ordering of subsets of l, obtained by interpreting these subsets as binary string representations of ...