NumberOfKPaths[g, v, k] returns a sorted list that contains the number of paths of length k to different vertices of g from v.NumberOfKPaths[al, v, k] behaves identically, ...

NumberOfNecklaces[n, nc, Cyclic] returns the number of distinct ways in which an n-bead necklace can be colored with nc colors, assuming that two colorings are equivalent if ...

OrbitInventory[ci, x, w] returns the value of the cycle index ci when each formal variable x[i] is replaced by w. OrbitInventory[ci, x, weights] returns the inventory of ...

OrbitRepresentatives[pg, x] returns a representative of each orbit of x induced by the action of the group pg on x.

Orbits[pg, x] returns the orbits of x induced by the action of the group pg on x.

PartialOrderQ[g] yields True if the binary relation defined by edges of the graph g is a partial order, meaning it is transitive, reflexive, and antisymmetric. ...

RankKSetPartition[sp, s] ranks sp in the list of all k-block set partitions of s. RankSetPartition[sp] ranks sp in the list of all k-block set partitions of the set of ...

SetEdgeLabels[g, l] assigns the labels in l to edges of g.

SetPartitionListViaRGF[n] lists all set partitions of the first n natural numbers, by first listing all restricted growth functions (RGFs) on these and then mapping the RGFs ...

SetVertexLabels[g, l] assigns the labels in l to vertices of g.