Segments of G-systems

  1. kernels of systems G(n,k) rewritten to more general form [k]
  2. particular segments #s of system [k] (where s= 0..n-1) build the systems G(n,k)

System [2]:

 #0     00
 ---------------------------------
        10      01
 #1     11
 ---------------------------------
        20      02
        21      12
 #2     22
 ---------------------------------
        30      03
        31      13
        32      23
 #3     33
 ---------------------------------
        40      04
        41      14
        42      24
        43      34
 #4     44

System [3]:

 #0    000
 ---------------------------------
       100     001     010
       110     101     011
 #1    111
 ---------------------------------
       200     002     020
       201     012     120
       210     102     021
       211     112     121
       220     202     022
       221     212     122
 #2    222
 ---------------------------------
       300     003     030
       301     013     130
       302     023     230
       310     103     031
       311     113     131
       312     123     231
       320     203     032
       321     213     132
       322     223     232
       330     303     033
       331     313     133
       332     323     233
 #3    333

System [4]:

 #0   0000
 ---------------------------------
      1000    0001    0010    0100
      1010    0101
      1100    1001    0011    0110
      1110    1101    1011    0111
 #1   1111
 ---------------------------------
      2000    0002    0020    0200
      2001    0012    0120    1200
      2010    0102    1020    0201
      2011    0112    1120    1201
      2020    0202
      2100    1002    0021    0210
      2101    1012    0121    1210
      2110    1102    1021    0211
      2111    1112    1121    1211
      2120    1202    2021    0212
      2121    1212
      2200    2002    0022    0220
      2201    2012    0122    1220
      2210    2102    1022    0221
      2211    2112    1122    1221
      2220    2202    2022    0222
      2221    2212    2122    1222
 #2   2222

Schematic algebra