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BELL SYSTEM TECHNICAL JOURNAL 



course, group invariance can often be recognized directly from circuit re- 

 quirements in a design problem. 



Tables I and TI have been constructed for cases where a relation exists 

 involving two or three variables. To illustrate their use, suppose we have 

 a function such that 



A^111^312/ = / 



Fig. 24 — M network for partiall>' symmetric functions. 



The corresponding entry Z'Y'X in the group table refers us to circuit 9 of 

 Fig. 23. The asterisk shows that the circuit may be used directly; if there 

 is no asterisk an interchange of variables is required. We expand f about 

 X, Y, Z and only two different functions will appear in the factors. These 

 two functions are realized with two trees extending from the terminals of the 

 network 9. Any such function/ can be realized with (using just one variable 

 in the A^ network) 



9 + 2(2"-' - 2) -t- 2 



+ 7 



elements, 



