simple stuff

[Wouter Meeussen]

Christian,

could you check on my calculation that the  permutations of
{-1,-1,-1,-1, 1, 1, 1, 1} under symmetry conditions of
rotation through 2n positions (here n=4)
and
(-1) <--> (+1) exchange

give

n       tot     # distinct      count*degeneracy
1       2       1               1*2
2       6       2               1*2+1*4
3       20      3               1*2+1*6+1*12
4       70      7               1*2+1*4+2*8+3*16
5       252     15              1*2+3*10+11*20
6       924     44              1*2+1*4+1*6+6*12+35*24
7       3432    128             1*2+9*14+118*28
8       12870   415             1*2+1*4+2*8+19*16+392*32
9       48620   1367            1*2+1*6+1*12+28*18+1336*36

resulting in a # of distinct permutations of
{1,2,3,7,15,44,128,415,1367,...}




NV Vandemoortele Coordination Center
Oils & Fats Applied Research
Prins Albertlaan 79
Postbus 40
B-8870 Izegem (Belgium)
Tel: +/32/51/33 21 11
Fax: +/32/51/33 21 75
vdmcc at vandemoortele.be