158 
0 if» >u 
TAH Av =| oy oen (71) 
the sum of all ,/ being the identical operator. A, can be written 
as a multiple sum of the operators ,/,...., ,J: 
Seat Seals | 
A= = mr (72) 
w Oow 
When now we write 
Ply Rea, aie ree ah (73) 
and 
pete A... (74) 
we have for a+ 8>4 and for «e+8=4, a #8 certainly u < v, 
while w=v for e+8=4, a=f. For u<v however we have: 
2h. k 
Qu. VEA 2 k Qu OE OE 2u 
P=A,P=A, > ,JP= S yl A,P= Ay > Sy wl AyP . (75) 
w w 
Ww 
while for a+ 8=—=4 and a=8 we have u=v: 
gaÂ = 902A. (76) 
au. 
Hence P is for a + 824 always a sum of quantities all alternating 
in u systems of two factors. Their number is the number of simple 
alternations ,24. We consider of these quantities an arbitrary one 
and call the corresponding operator, of which this quantity is built 
2u 
up from P: O,. Then: 
Del 
Og Ars Eads liefe FP ore PRE Alu Se an 
QO, = A, fatg=4, u=v. 
We then have: 
-_~ 
— _ _~ 2u 2h 
(Ma. 75.) (Cb... 'b) (Aa... -'a)(@b....'b) = S(O, P) P 
7 
(78) 
Since, however, the a and b are all equivalent, we apparently 
have for each simple alternation 
2u 2p 2 2p 2 2u 
(Ay P) P =P (Ay P) = (A, P) (A; P) (79) 
and in consequence, since ,,/ can be written as a multiple sum of 
alternations : 
2u 2p Qu. 2p 
(0, P)P = (0, P) (0, P). (80) 
Now we have according to (65) and (66) 
