10 
THE SYMMETRIC FUNCTION TABLES OF THE FIFTEENTHIC. 
Tenthic—continued: 
In 1881 a formula giving the number of symmetric functions of a 
given weight was announced by Forsyth. 8 An application of it, to get 
an idea of the lengths of tables not then computed, gives the number of 
symmetric functions of weight 15 to be 176, of weight 22 to be 1001, and 
of weight 30 to be 5595. 
Hammond, in the Proceedings of the London Mathematical Society 
for 1881-82 (vol. 13), gives a convenient method for calculating those 
terms in [x x z 2 . . . * n ] which contain no a with a subscript greater than 
a given number by identifying the coefficients with coefficients in tables 
of lower weight. Thus 
[54321] =a 5 
X (terms in [4321] containing no a with a subscript greater than 5) 
+ terms containing a’s with subscripts greater than 5: 
that is 
[54321] = a 5 X 
[ (4321) — 3 (43 2 ) — 3 (4 2 1 2 ) -f 4 (4 2 2) — 3 (52 2 1) + 4 (531 2 ) + 5 (532) — 5 (5 2 ) ] 
+ terms containing a’s with subscripts greater than 5. 
He also gives a formula for the computation of symmetric functions 
by the use of auxiliary functions. 
A. R. Forsyth: Messenger of Mathematics, vol. 10, 1880-81. 
