516 
MAJOR MACMAHOR OR SYMMETRIC FURCTIORS 
Hence 
(3l H) = A [(H To) (H) — (21 01) (To) — (To oT) (2T) + (2T To oT)} ; 
and it is easy to see that A = — for each of the products (21 01) (iO), (10 01) (21) 
on multiplication produces a term + (31 01), and this monomial is not produced by 
the development of either of the other two products. The value of A may, however, 
be instructively obtained by means of the operator 
For 
ffoi (FT 01) = (IT), 
and 
5^01 — i^(oi) — 3(oi) “h (lb) 9(iooi) “h (21) 8(21 m) “h (21 10) 0(2i Jo oi)- (Art, 53.) 
Hence 
(H) = 2 A { - (H) (To) + (H To)], 
and now A is obviously equal to — 
But we may further employ the operator 
For 
(/si = — Gsi +•••=+ 5^(21 lo) + • • • (Arts. 17, 53), 
significant terms only being retained; hence — G31 and To) = 0(2ilo) equivalent 
operations in the present case, and performing them on their own sides — 1 = 2A. or 
Thus 
(3l oT) = - 1 (2T To) (oT) + 1 (h oT) (To) + i (To oT) ( 2 T) - i (HT To bl). 
§ 10. The Partition ohliterating Operators. 
60. In the foregoing a generalisation has been made from a number to the partition 
of a number in the case of the operations g^Q, g^^, . . , gp^, . . . The possibility of the 
like generalisation in respect of the obliterating operators Gloj, . . . G^^, ... is 
naturally presented as a subject for enquiry. 
Consider a symmetric function 
f (*^10’ 
to be the product of m monomial functions, and write 
/ = /l/3 • • • fm- 
