THEORY OF THE PARTITION OF NUMBERS. 
655 
(3) unipartite partitions, containing p parts and a highest figure r. 
(4) ?’-partite partitions, containing p parts and a highest figure 1. 
(5) unipartite partitions, containing r parts and a highest figure y>. 
(6) p>-partite partitions, containing r parts and a highest figure 1. 
In this enunciation we may substitute for r or p, or for both, the phrases “ not 
exceeding r.” “not exceeding p.” 
Art. 48. For a given number of nodes, in the simplest cases, it will be suitable to 
view the graphs of the graphically regularised partitions. 
Omitting the trivial case of a single node, we have 
Number 2. 
• • 
9 
• 
0 
(2) 
(TT) 
(11) 
Number 3. 
e © • • • 
• 
0 « • 
• 
• 
0 
• 
<§> 
<3) m 
(21) (U1) 
(ff 10) 
(111) 
Number 4. 
• © • # • © ® 
(S) • • • • 
• 
• 
0 • • 
• • 
• (§)• 
e 
(1) (81) 
(31) (211) (21 10) 2: 
2 (211) 
0® 
9 
• 
• 
® <D 
• 
• 
© 
0 
(H 
(22) (mi) 
(111 100) (11 10 10) 
(ii u) 
(1111) 
The table is continued in an 
obvious manner. The essentially distinct graphs 
for the 
Number 2. 
Number 3. 
