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The action on
the set of edges |
The action on the set of edges
When labelling the edges of the fullerene C60 as is
indicated in table the
generators of the induced permutation group on the set of edges of
the fullerene are given by:
π1=
(86,87,88,89,90)(81,82,83,84,85)(72,74,76,78,80)(71,73,75,77,79)(58,61,64,67,70)
(57,60,63,66,69)(56,59,62,65,68)(43,46,49,52,55)(42,45,48,51,54)(41,44,47,50,53)
(36,37,38,39,40)(27,29,31,33,35)(26,28,30,32,34)(13,16,19,22,25)(12,15,18,21,24)
(11,14,17,20,23)(6,7,8,9,10)(1,2,3,4,5)
π2=
(51,67,78,77,66)(50,52,68,84,65)(33,69,90,76,39)(32,40,79,89,64)(22,54,86,75,31)
(21,53,85,83,49)(20,34,80,88,48)(19,23,70,87,63)(13,27,37,28,14)(10,55,81,62,18)
(9,24,56,82,47)(7,12,43,44,15)(6,41,59,46,8)(5,36,72
,61,17)(4,35,71,74,30)
(3,25,57,73,38)(2,11,42,60,29)(1,26,58,45,16)
σ=
(88,89)(87,90)(86)(83)(82,84)(81,85)(75,76)(74,77)(73,78)(72,79)(71,80)(63,64)
(62,65)(61,66)(60,67)(59,68)(58,69)(57,70)(56)(48)(47,49)(46,50)(45,51)(44,52)(43,53)
(42,54)(41,55)(38,39)(37,40)(36)(30,31)(29,32)(28,33)(27,34)(26,35)(18)(17,19)(16,20)
(15,21)(14,22)(13,23)(12,24)(11,25)(8,9)(7,10)(6)(3)(2,4)(1,5) The
cycle indices for the corresponding actions on the set of edges are
given as
| Z(R,Edges)=.. |
1
60
|
(24 x518
+20 x330 +15 x12
x244 +x190) .. |
| Z(S,Edges)=.. |
1
120
|
( 24 x109
+20 x615 +24 x518 +20
x330 +x245 +15
x12 x244 +15
x18 x241
+x190). .. |
harald.fripertinger "at" uni-graz.at, May 10,
2016
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The action on
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