GENERATING FUN'CTIONS IN THE THEORY OF NUMBERS. 
157 
The portion is a permutation of 
/y» 2/y» S'V* /y» ry* 3/-y» 
• • • • • • 
and we can obtain this portion by selecting for multiplication 
2 elements from the row appertaining to the exponent 
3 
33 
35 
33 
33 
^^0 - 
33 
55 ^2 
1 
35 
33 
35 
3 3 
33 
55 ^3 
1 
35 
33 
33 
35 
3 5 
55 ^4 
3 
35 
33 
33 
33 
33 
55 I’s 
1 
35 
3 5 
33 
3 5 
33 
55 ^8 
The permutation is divided into five compartments as shown. 
In the first compartment we have simply Xo which is to be taken from the 2nd row 
2nd column. In the second compartment we have 
/y* /y 
which is obtainable by multiplication of elements taken from the 4th, 2nd, and 1st 
rows, as follows ;— 
In row 4, column 2, we take ^ ‘ — 
9 1 1 
5) ■"> -*•> 55 -*■ 
55 I5 55 4 , ,, fx^^x^x.^x^x-^^ ; 
multiplication gives 
^ 4 . 2 ^ 31 ^ 4 ^ 2^1 • 
In the third compartment we find 
/y ryt /y> /y» 
From row 8, column 5, 
we take 
^85 1 
M'HB ^7^6 
5) 
5 ^ 
? 3 
33 
5, 
3, 
2 , 
1 , 
5, 9, 
33 2j ,, 
3 3 ^3 3 5 
Q 
33 ^3 53 
^ A 
/^53 •'^4 
1 . 
1 . 
11 fY* 'V* 'Y* 'Y 'Y* Y* Y* Y* 
Multiplication of these five elements yields 
