[metzler] 



SOME NEW SYMMETRIC FUNCTION TABLES 



2 77 



+ ^Pi P, + 12Pî Pt + S Pi p, p, + 3 p, p, p,) + p^ {px P, p, + 3 Pi 

 PiPe - '2 Pi p\ - Pt P% P^^ P\ ^ P\ Pt + P\ P\ + Pi P[p, - '^ P\ Pz Pi 

 - p\ V2 Pt) + pI (P2 P, - Pi VÙ- 



9. That the law for the determinants in art. 7 is general may be 

 shown by means of the operator P. For since 



P 2 a, 



aj, 



Pi 2 ai aj . . . au-i 



the coefficient of Pi in P Dy^ is evidently the coefficient of Pij^\ in 

 Djç plus the result of operating on the coefficient of pi by P, that is 



Sk-i-l 



(-1) 



where the first determinant is of order ^A — t — i and the second of 

 order 2k — i. If we operate by P in the second term by rows we get 

 the sum of 2 k — i determinants which are as follows : 



