NecklacePolynomial[n, c, Cyclic] returns a polynomial in the colors in c whose coefficients represent numbers of ways of coloring an n-bead necklace with colors chosen from ...

NthPair[n] returns the n\[Null]^th unordered pair of distinct positive integers, when sequenced to minimize the size of the larger integer. Pairs that have the same larger ...

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. ...

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, ...

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. ...