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13. PRS subworld

The next subworld of P-world is PRS-subworld. Links belonging to it are obtained replacing digons in source links of P-world by RS-tangles. The symmetry rules determining such substitutions are the same as in PR *-subworld. 

The same as in Table 8, the representatives of source links derived from 6* are: .2, .2.2, .2.2.2, .2.2.20, 2:2:2, .2.2.2.2, .2.2.2.20, .2.2.20.20 2.2.2.2 and 2.2.20.2. The generating PRS-links derived from them are given in Table 11: 

Table 11 
 

n=9  .(2,2) 
n=10  .(~3 *,2)  .(2,2).2 
.(2,2)1 
.(2,2+) 
n=11  .(2,2,2)  .(~3 *,2).2  .(2,2).2.2  .(2,2).2.20  (2,2):2:2 
.(~4 *,2)  .(2,~3 *).2  .2.(2,2).2  .2.(2,2).20 
.(~3 ^,~3 ^ .(2,2).~3 *  .2.2.(2,2)0 
.(~3 *,2)1  .(2,2+).2 
.(2,2)~
.(~3 *,2+) 
.(2,2+)1 
.(2,2++) 
n=12  .(~3 *,2,2)  .(2,2,2).2  .(~3 *,2).2.2  .(~3 *,2).2.20  (~3 *,2):2:2 
.(2,2,2)1  .(~4 *,2).2  .(2,~3 *).2.2  .(2,~3 *).2.20  (2,2):~3 *:2 
.(2,2,2+)  .(2,~4 *).2  .2.(~3 *,2).2  .2.(~3 *,2).20  (2,2)1:2:2 
.(~5 *,2)  .(~3 ^,~3 ^).2  .(2,2).~3 *.2  .2.(2,~3 *).20  (2,2+):2:2 
.(~4 *,~3 * .(~3 *,2)1.2  .(2,2).2.~3 *  .2.2.(~3 *,2)0 
.(~4 *,2)1  .(2,~3 *)1.2  .~3 *.(2,2).2  .2.2.(2,~3 *)0 
.(~3 ^,~3 ^)1  .(2,2)~2.2  .(2,2)1.2.2  .(2,2)1.2.20 
.(~3 *,2)~ .(~3 *,2).~3 *  .2.(2,2)1.2  .2.(2,2)1.20 
.(2,2)~ .(2,~3 *).~3 *  .(2,2+).2.2  .2.2.(2,2)10 
.(~4 *,2+)  .(2,2).~4 *  .2.(2,2+).2  .(2,2).~3 *.20 
.(~3 ^,~3 ^+)  .(2,2).(2,2)  .(2,2).2.~3 *
.(~3 *,2+)1  .(~3 *,2+).2  .~3 *.(2,2).20 
.(2,2+)~ .(2,~3 *+).2  .2.(2,2).~3 *
.(~3 *,2++)  .(2,2+).~3 *  .~3 *.2.(2,2)0 
.(2,2++)1  .(2,2++).2  .2.~3 *.(2,2)0 
.(2,2+).2.20 
.2.(2,2+).20 
.2.2.(2,2+)0 
n=12  .(2,2).2.2.2  .(2,2).2.2.20  .(2,2).2.20.20  (2,2).2.2.2  (2,2).2.20.2 
.2.(2,2).2.20  2.(2,2).2.2  2.(2,2).20.2 
.2.2.(2,2).20  2.2.20.(2,2) 
.2.2.2.(2,2)0 

In the same way, from the representatives 8*2, 8*2.2 and 8*2.20 (Table 9) we derive for n = 11 generating link 8*(2,2), and for n = 12 generating links 8*(~3 *,2), 8*(2,2)1, 8*(2,2+), 8*(2,2).2, 8*(2,2).20, 8*2.(2,2)0. From the representative 9*2 (Table 10) we derive for n = 12 generating link 9*(2,2). 

 

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