548 
MATHEMATICS: H. B. FINE 
where Fj is the value of F for (x^, Xj, . . . , Xn) = (x^^y x^/^y . . . 4^0, 
and Ai^^ the cof actor of the element in the ith row and the ^th 
column of Fj. But 
Hence 
(S) 
and therefore 
Pj^nn <f)j. 
Again, the expressions under the summation sign in the equations 
(3) are of the form 
2 ciki b 
and 
\ /=1 / ( k=l \ 1=1 / ) I )fe=l 
(6) 
where a denotes the greatest of the numbers | a,-^ 
Hence 
2 i n U _3 2 
32 
and therefore 
From (5) and (7) it follows that 
<Pj+i ^ ^1 where 
Pj+i ^ ^2 Pi, where ^2 = — = — t~ 
Hence ^i^y+i^ {k].<Pjf and therefore, by setting ^ = 0, 1,2, 
cessively, 
(7) 
(8) 
(9) 
sue- 
(10) 
