cycles.spad line 1 [edit on github]
Enumeration by cycle indices.
SFunction( is the li)S-function of the partition li
alternating n is the cycle index of the alternating group of degree n.
cap(s1, s2), introduced by Redfield, is the scalar product of two cycle indices.
complete n is the n th complete homogeneous symmetric function expressed in terms of power sums. Alternatively it is the cycle index of the symmetric group of degree n.
cup(s1, s2), introduced by Redfield, is the scalar product of two cycle indices, in which the power sums are retained to produce a cycle index.
cyclic n is the cycle index of the cyclic group of degree n.
dihedral n is the cycle index of the dihedral group of degree n.
elementary n is the n th elementary symmetric function expressed in terms of power sums.
eval s is the sum of the coefficients of a cycle index.
graphs n is the cycle index of the group induced on the edges of a graph by applying the symmetric function to the n nodes.
powerSum n is the n th power sum symmetric function.
skewSFunction(li1, li2) is the S-function of the partition difference li1 - li2 expressed in terms of power sum symmetric functions.
wreath(s1, s2) is the cycle index of the wreath product of the two groups whose cycle indices are s1 and s2.