A multi-dimensional cycle index |

Replacing in such a situation the cycle index ofX:=È_{i=1}^{n}X_{i}.

whereZ_{n}(G,X_{1}È...ÈX_{n}):=(1)/(|G|)å_{gÎG}Õ_{i=1}^{n}(Õ_{j=1}^{|Xi|}x_{i,j}^{ai,j(g)}),

Returning to the fullerene C* _{60}* the groups

andZ_{6}(R)=(1)/(60)( 24 v_{5}^{12}e_{5}^{12}E_{5}^{6}f_{1}^{2}f_{5}^{2}F_{5}^{4}d_{5}^{6}+ 20 v_{3}^{20}e_{3}^{20}E_{3}^{10}f_{3}^{4}F_{1}^{2}F_{3}^{6}d_{3}^{10}+ 15 v_{2}^{30}e_{2}^{30}E_{1}^{2}E_{2}^{14}f_{2}^{6}F_{2}^{10}d_{1}^{2}d_{2}^{14}+ v_{1}^{60}e_{1}^{60}E_{1}^{30}f_{1}^{12}F_{1}^{20}d_{1}^{30})

From these cycle indices we deduce that the action on the sets of vertices and pentagonal edges have the same cycle type. The variablesZ_{6}(S)=(1)/(2)Z_{6}(R)+(1)/(120)( 24 v_{10}^{6}e_{10}^{6}E_{10}^{3}f_{2}f_{10}F_{10}^{2}d_{5}^{6}+ 20 v_{6}^{10}e_{6}^{10}E_{6}^{5}f_{6}^{2}F_{2}F_{6}^{3}d_{3}^{10}+ 15 v_{1}^{4}v_{2}^{28}e_{1}^{4}e_{2}^{28}E_{1}^{4}E_{2}^{13}f_{1}^{4}f_{2}^{4}F_{1}^{4}F_{2}^{8}d_{1}^{2}d_{2}^{14}+ v_{2}^{30}e_{2}^{30}E_{2}^{15}f_{2}^{6}F_{2}^{10}d_{1}^{30}).

whereas the number of109700303821413736143664612170571163303931905179435773317873664

This substitution into an54850151910706868071832306128208569015853860985570356157743104.

`polya_multi_const_sub(a,b,c)`

.
harald.fripertinger@kfunigraz.ac.at,

last changed: January 23, 2001

A multi-dimensional cycle index |