AlternatingGroupIndex[n, x] gives the cycle index of the alternating group of size n permutations as a polynomial in the symbols x[1], x[2], ..., x[n]}.

AlternatingGroup[n] generates the set of even-size n permutations, the alternating group on n symbols. AlternatingGroup[l] generates the set of even permutations of the list ...

CodeToLabeledTree[l] constructs the unique labeled tree on n vertices from the Prüfer code l, which consists of a list of n - 2 integers between 1 and n.

CyclicGroupIndex[n, x] returns the cycle index of the cyclic group on n symbols, expressed as a polynomial in x[1], x[2], ..., x[n].

DihedralGroupIndex[n, x] returns the cycle index of the dihedral group on n symbols, expressed as a polynomial in x[1], x[2], ..., x[n].

SymmetricGroupIndex[n, x] returns the cycle index of the symmetric group on n symbols, expressed as a polynomial in x[1], x[2], ..., x[n].

Wheel[n] constructs a wheel on n vertices, which is the join of CompleteGraph[1] and Cycle[n - 1].

NFourierCoefficient[expr, t, n] gives a numerical approximation to the n \[Null]^th coefficient in the Fourier exponential series expansion of expr, where expr is a periodic ...

Mathematica provides flexible mechanisms for full typeset formatting of numbers of any magnitude and precision, to optimize readability, portability, and external ...

Mathematica's symbolic architecture allows it to represent any equation as a symbolic expression that can be manipulated using any of Mathematica's powerful collection of ...