# Principalities and dominions of 3-ary Boolean functions
### faction size 1

king index 0 (king 0) :
| principality | principality | dominion | dominion |
| truth tables | Zhegalkin indices | truth tables | Zhegalkin indices |
| (0) | (0) | (0) | (0) |
king index 104 (king 26752) :
| principality | principality | dominion | dominion |
| truth tables | Zhegalkin indices | truth tables | Zhegalkin indices |
| (104) | (232) | (150) | (22) |

### faction size 3

king index 6 (king 1632) :
| principality | principality | dominion | dominion |
| truth tables | Zhegalkin indices | truth tables | Zhegalkin indices |
| (6) (18) (20) | (102) (90) (60) | (96) (72) (40) | (96) (72) (40) |
king index 110 (king 28384) :
| principality | principality | dominion | dominion |
| truth tables | Zhegalkin indices | truth tables | Zhegalkin indices |
| (110) (122) (124) | (142) (178) (212) | (246) (222) (190) | (118) (94) (62) |

### faction size 4

king index 22 (king 5760) :
| principality | principality | dominion | dominion |
| truth tables | Zhegalkin indices | truth tables | Zhegalkin indices |
| (22) | (150) | (232) | (104) |
| (24) (36) (66) | (120) (108) (106) | (120) (108) (106) | (24) (36) (66) |
king index 42 (king 10920) :
| principality | principality | dominion | dominion |
| truth tables | Zhegalkin indices | truth tables | Zhegalkin indices |
| (126) | (126) | (126) | (126) |
| (42) (76) (112) | (130) (132) (144) | (252) (250) (238) | (84) (50) (14) |

### faction size 6

king index 8 (king 2176) :
| principality | principality | dominion | dominion |
| truth tables | Zhegalkin indices | truth tables | Zhegalkin indices |
| (8) (32) (64) | (136) (160) (192) | (240) (204) (170) | (16) (4) (2) |
| (40) (72) (96) | (40) (72) (96) | (60) (90) (102) | (20) (18) (6) |
king index 14 (king 3808) :
| principality | principality | dominion | dominion |
| truth tables | Zhegalkin indices | truth tables | Zhegalkin indices |
| (14) (50) (84) | (238) (250) (252) | (144) (132) (130) | (112) (76) (42) |
| (60) (90) (102) | (20) (18) (6) | (20) (18) (6) | (60) (90) (102) |

### faction size 12

king index 2 (king 680) :
| principality | principality | dominion | dominion |
| truth tables | Zhegalkin indices | truth tables | Zhegalkin indices |
| (2) (4) (16) | (170) (204) (240) | (192) (160) (136) | (64) (32) (8) |
| (30) (54) (86) | (30) (54) (86) | (24) (36) (66) | (120) (108) (106) |
| (10) (12) (34) (48) (68) (80) | (34) (68) (10) (80) (12) (48) | (48) (80) (12) (68) (10) (34) | (80) (48) (68) (12) (34) (10) |
king index 26 (king 6856) :
| principality | principality | dominion | dominion |
| truth tables | Zhegalkin indices | truth tables | Zhegalkin indices |
| (26) (28) (38) (52) (70) (82) | (210) (180) (198) (156) (166) (154) | (184) (216) (172) (228) (202) (226) | (88) (56) (100) (44) (98) (74) |
| (46) (58) (78) (92) (114) (116) | (78) (114) (46) (116) (58) (92) | (92) (116) (58) (114) (46) (78) | (116) (92) (114) (58) (78) (46) |
king index 44 (king 11464) :
| principality | principality | dominion | dominion |
| truth tables | Zhegalkin indices | truth tables | Zhegalkin indices |
| (62) (94) (118) | (190) (222) (246) | (212) (178) (142) | (124) (122) (110) |
| (106) (108) (120) | (66) (36) (24) | (86) (54) (30) | (86) (54) (30) |
| (44) (56) (74) (88) (98) (100) | (228) (216) (226) (184) (202) (172) | (156) (180) (154) (210) (166) (198) | (52) (28) (82) (26) (70) (38) |

### overview

dominion :
| truth tables | Zhegalkin indices | truth tables | Zhegalkin indices |