# Families of Boolean functions

Boolean functions belong to the same family, when they can be transformed into each other by negating arguments. The size of a family is always a power of two. The maximal size is 2, i.e. the period length of the truth table. (While the size of faction and clan increases with the chosen arity, the size of a family is fixed.)
The simplest property of a family is its weight, i.e. the number of true entries in each truth table. An important property is the parity of the weight. Those with odd weight shall be called sharp, those with even weight blunt. (It is the same as the parity of the quaestor weight.)
A family belongs to a clan (where the arguments are not just negated, but also permuted). Together with its complement, it forms a super-family. Adding a half-complement forms an ultra-family.

## family matrix

A family matrix is a bitwise XOR table with integers replaced by binary values. Each row (or column) is the truth table of a Boolean functions in the family.
| bitwise XOR table with labels on the left showing how the arguments are negated | red family matrix of a 4-ary function, containing each function twice | eight members of a family as Venn diagrams and rows of a family matrix | two family matrices of 3-ary seals, one with 4 functions (left), the other with 2 (right) |

## sequences

arity to count :
| | | | arity $n$ | arity $n$ | arity $n$ | arity $n$ | arity $n$ | arity $n$ |
| | | | 0 | 1 | 2 | 3 | 4 | 5 |
| | | balanced families (central values of A054724) | 0 | 1 | 3 | 14 | 870 | 18796230 |
| ${\frac {(2^{2^{n-1}})(2^{n}-1)}{2^{n}}}$ | Mint | introverted families | 0 | 1 | 3 | 14 | 240 | 63488 |
| ${\frac {2^{2^{n}}}{2^{n}}}~=~2^{(2^{n}-n)}$ | DubSage | extroverted families (BF with a particular consul) | 2 | 2 | 4 | 32 | 4096 | 134217728 |
| $2^{n}-n-1$ | | Eulerian numbers | 0 | 0 | 1 | 4 | 11 | 26 |
| ${\frac {2^{2^{n}}}{2^{n{\color {Red}+1}}}}~=~2^{(2^{n}-n-1)}$ | Sage | sharp families (BF with a particular prefect) | 1 | 1 | 2 | 16 | 2048 | 67108864 |
| ${\frac {2^{2^{n}}+(2^{2^{n-1}{\color {Red}+1}})(2^{n}-1)}{2^{n{\color {Red}+1}}}}$ | Balm | blunt families super-families | 1 | 2 | 5 | 30 | 2288 | 67172352 |
| ${\frac {2^{2^{n}}+(2^{2^{n-1}})(2^{n}-1)}{2^{n}}}$ | Thyme | families | 2 | 3 | 7 | 46 | 4336 | 134281216 |
| | TornSage | sharp super-families | | 1 | 1 | 8 | 1024 | 33554432 |
| | Clove | blunt super-families | | 1 | 4 | 22 | 1264 | 33617920 |
| | Aloe | families with maximal size $2^{n}$ (right column of Olive) | 2 | 1 | 2 | 23 | 3904 | 134156284 |
| | | blunt families with maximal size $2^{n}$ | 1 | 0 | 0 | 7 | 1856 | 67047420 |
family representatives :
| n | | sequence |
| 0 | 2 | 0, 1, |
| 1 | 1 | 2, |
| 2 | 4 | 4, 6, 8, 9, |
| 3 | 39 | 16, 18, 20, 22, 24, 32, 33, 36, 40, 41, 44, 64, 65, 66, 72, 73, 74, 96, 97, 98, 104, 106, 107, 128, 129, 130, 131, 132, 133, 134, 135, 144, 145, 146, 147, 148, 149, 150, 151, |
| 4 | 4290 | 256, 258, 260, 262, 264, 272, 274, 276, 278, 280, 288, 292, 296, 300, 320, 322, 328, 330, 352, 354, 360, 362, 384, 386, 388, 390, 400, 402, 404, 406, 512, 513, 516, 520, 521, 524, 528, 532, 536, 540, 544, 545, 548, 552, 553, 556, 560, 564, 568, 572, 576, 577, 584, 585, 608, 609, 616, 617, 640, 641, 644, 645, 656, 657, 660, 661, 704, 705, 708, 709, 720, 721, 724, 725, 1024, 1025, 1026, 1032, 1033, 1034, 1040, 1042, 1048, 1050, 1056, 1057, 1064, 1065, 1088, 1089, 1090, 1096, 1097, 1098, 1104, 1106, 1112, 1114, 1120, 1121, 1128, 1129, 1152, 1153, 1154, 1155, 1168, 1169, 1170, 1171, 1184, 1185, 1186, 1187, 1200, 1201, 1202, 1203, 1536, 1537, 1538, 1544, 1546, 1547, 1552, 1554, 1560, 1562, 1568, 1569, 1576, 1577, 1600, 1601, 1608, 1609, 1632, 1633, 1634, 1640, 1642, 1643, 1648, 1650, 1656, 1658, 1664, 1665, 1666, 1667, 1680, 1681, 1682, 1683, 1696, 1697, 1698, 1699, 1712, 1713, 1714, 1715, 2048, 2049, 2050, 2051, 2052, 2053, 2054, 2055, 2064, 2066, 2068, 2070, 2080, 2081, 2084, 2085, 2096, 2097, 2100, 2101, 2112, 2113, 2114, 2115, 2128, 2129, 2130, 2131, 2144, 2145, 2146, 2147, 2160, 2161, 2162, 2163, 2176, 2177, 2178, 2179, 2180, 2181, 2182, 2183, 2192, 2194, 2196, 2198, 2208, 2209, 2212, 2213, 2224, 2225, 2228, 2229, 2240, 2241, 2242, 2243, 2256, 2257, 2258, 2259, 2272, 2273, 2274, 2275, 2288, 2289, 2290, 2291, 2304, 2305, 2306, 2307, 2308, 2309, 2310, 2311, 2320, 2322, 2324, 2326, 2336, 2337, 2340, 2341, 2352, 2353, 2356, 2357, 2368, 2369, 2370, 2371, 2384, 2385, 2386, 2387, 2400, 2401, 2402, 2403, 2416, 2417, 2418, 2419, 2432, 2434, 2436, 2438, 2448, 2449, 2450, 2451, 2452, 2453, 2454, 2455, 2464, 2465, 2468, 2469, 2480, 2481, 2484, 2485, 2496, 2497, 2498, 2499, 2512, 2513, 2514, 2515, 2528, 2529, 2530, 2531, 2544, 2545, 2546, 2547, 4096, 4097, 4098, 4100, 4102, 4104, 4105, 4128, 4129, 4130, 4132, 4134, 4136, 4137, 4160, 4161, 4162, 4164, 4166, 4168, 4169, 4192, 4193, 4194, 4196, 4198, 4200, 4201, 4224, 4225, 4226, 4227, 4228, 4229, 4230, 4231, 4232, 4233, 4234, 4235, 4236, 4237, 4238, 4239, 4608, 4609, 4610, 4612, 4614, 4616, 4617, 4640, 4642, 4643, 4644, 4646, 4648, 4649, 4672, 4673, 4680, 4681, 4682, 4684, 4686, 4704, 4705, 4712, 4714, 4715, 4716, 4718, 4736, 4737, 4738, 4739, 4740, 4741, 4742, 4743, 4744, 4745, 4746, 4747, 4748, 4749, 4750, 4751, 5120, 5121, 5122, 5124, 5126, 5128, 5129, 5152, 5153, 5160, 5161, 5162, 5164, 5166, 5184, 5186, 5188, 5189, 5190, 5192, 5193, 5216, 5217, 5224, 5226, 5228, 5229, 5230, 5248, 5249, 5250, 5251, 5252, 5253, 5254, 5255, 5256, 5257, 5258, 5259, 5260, 5261, 5262, 5263, 5632, 5633, 5634, 5636, 5638, 5640, 5641, 5664, 5665, 5672, 5674, 5675, 5676, 5678, 5696, 5697, 5704, 5706, 5708, 5709, 5710, 5728, 5730, 5732, 5734, 5735, 5736, 5737, 5760, 5761, 5762, 5763, 5764, 5765, 5766, 5767, 5768, 5769, 5770, 5771, 5772, 5773, 5774, 5775, 6144, 6145, 6146, 6147, 6148, 6149, 6150, 6151, 6152, 6153, 6154, 6155, 6156, 6157, 6158, 6159, 6176, 6177, 6178, 6179, 6180, 6181, 6182, 6183, 6184, 6185, 6186, 6187, 6188, 6189, 6190, 6191, 6208, 6209, 6210, 6211, 6212, 6213, 6214, 6215, 6216, 6217, 6218, 6219, 6220, 6221, 6222, 6223, 6240, 6241, 6242, 6243, 6244, 6245, 6246, 6247, 6248, 6249, 6250, 6251, 6252, 6253, 6254, 6255, 6272, 6273, 6274, 6275, 6276, 6277, 6278, 6279, 6280, 6281, 6282, 6283, 6284, 6285, 6286, 6287, 6304, 6305, 6306, 6307, 6308, 6309, 6310, 6311, 6312, 6313, 6314, 6315, 6316, 6317, 6318, 6319, 6336, 6337, 6338, 6339, 6340, 6341, 6342, 6343, 6344, 6345, 6346, 6347, 6348, 6349, 6350, 6351, 6368, 6369, 6370, 6371, 6372, 6373, 6374, 6375, 6376, 6377, 6378, 6379, 6380, 6381, 6382, 6383, 8192, 8193, 8194, 8195, 8196, 8198, 8200, 8201, 8204, 8205, 8208, 8209, 8210, 8211, 8212, 8214, 8216, 8217, 8220, 8221, 8256, 8257, 8258, 8259, 8260, 8261, 8262, 8263, 8264, 8265, 8266, 8267, 8268, 8269, 8270, 8271, 8320, 8321, 8322, 8323, 8324, 8326, 8328, 8329, 8332, 8333, 8336, 8337, 8338, 8339, 8340, 8342, 8344, 8345, 8348, 8349, 8384, 8385, 8386, 8387, 8388, 8389, 8390, 8391, 8392, 8393, 8394, 8395, 8396, 8397, 8398, 8399, 8448, 8449, 8450, 8451, 8452, 8454, 8456, 8457, 8460, 8461, 8464, 8465, 8466, 8467, 8468, 8470, 8472, 8473, 8476, 8477, 8512, 8513, 8514, 8515, 8516, 8517, 8518, 8519, 8520, 8521, 8522, 8523, 8524, 8525, 8526, 8527, 8576, 8578, 8580, 8581, 8582, 8583, 8584, 8585, 8588, 8589, 8592, 8594, 8596, 8597, 8598, 8599, 8600, 8601, 8604, 8605, 8640, 8641, 8642, 8643, 8644, 8645, 8646, 8647, 8648, 8649, 8650, 8651, 8652, 8653, 8654, 8655, 9216, 9217, 9218, 9219, 9220, 9221, 9222, 9223, 9224, 9225, 9226, 9227, 9228, 9229, 9230, 9231, 9232, 9233, 9234, 9235, 9236, 9237, 9238, 9239, 9240, 9241, 9242, 9243, 9244, 9245, 9246, 9247, 9280, 9281, 9282, 9283, 9284, 9285, 9286, 9287, 9288, 9289, 9290, 9291, 9292, 9293, 9294, 9295, 9296, 9297, 9298, 9299, 9300, 9301, 9302, 9303, 9304, 9305, 9306, 9307, 9308, 9309, 9310, 9311, 9344, 9345, 9346, 9347, 9348, 9349, 9350, 9351, 9352, 9353, 9354, 9355, 9356, 9357, 9358, 9359, 9360, 9361, 9362, 9363, 9364, 9365, 9366, 9367, 9368, 9369, 9370, 9371, 9372, 9373, 9374, 9375, 9408, 9409, 9410, 9411, 9412, 9413, 9414, 9415, 9416, 9417, 9418, 9419, 9420, 9421, 9422, 9423, 9424, 9425, 9426, 9427, 9428, 9429, 9430, 9431, 9432, 9433, 9434, 9435, 9436, 9437, 9438, 9439, 10240, 10241, 10242, 10243, 10244, 10246, 10248, 10249, 10252, 10253, 10256, 10258, 10260, 10261, 10262, 10263, 10264, 10265, 10268, 10269, 10304, 10305, 10306, 10307, 10308, 10309, 10310, 10311, 10312, 10313, 10314, 10315, 10316, 10317, 10318, 10319, 10368, 10369, 10372, 10373, 10376, 10377, 10378, 10379, 10380, 10382, 10384, 10385, 10388, 10389, 10392, 10394, 10396, 10397, 10398, 10399, 10432, 10433, 10434, 10435, 10436, 10437, 10438, 10439, 10440, 10441, 10442, 10443, 10444, 10445, 10446, 10447, 10496, 10497, 10498, 10499, 10500, 10502, 10504, 10505, 10508, 10509, 10512, 10514, 10516, 10517, 10518, 10519, 10520, 10521, 10524, 10525, 10560, 10561, 10562, 10563, 10564, 10565, 10566, 10567, 10568, 10569, 10570, 10571, 10572, 10573, 10574, 10575, 10624, 10625, 10628, 10629, 10632, 10634, 10636, 10637, 10638, 10639, 10640, 10641, 10644, 10645, 10648, 10649, 10650, 10651, 10652, 10654, 10688, 10689, 10690, 10691, 10692, 10693, 10694, 10695, 10696, 10697, 10698, 10699, 10700, 10701, 10702, 10703, 11264, 11265, 11266, 11267, 11268, 11269, 11270, 11271, 11272, 11273, 11274, 11275, 11276, 11277, 11278, 11279, 11280, 11281, 11282, 11283, 11284, 11285, 11286, 11287, 11288, 11289, 11290, 11291, 11292, 11293, 11294, 11295, 11328, 11329, 11330, 11331, 11332, 11333, 11334, 11335, 11336, 11337, 11338, 11339, 11340, 11341, 11342, 11343, 11344, 11345, 11346, 11347, 11348, 11349, 11350, 11351, 11352, 11353, 11354, 11355, 11356, 11357, 11358, 11359, 11392, 11393, 11394, 11395, 11396, 11397, 11398, 11399, 11400, 11401, 11402, 11403, 11404, 11405, 11406, 11407, 11408, 11409, 11410, 11411, 11412, 11413, 11414, 11415, 11416, 11417, 11418, 11419, 11420, 11421, 11422, 11423, 11456, 11457, 11458, 11459, 11460, 11461, 11462, 11463, 11464, 11465, 11466, 11467, 11468, 11469, 11470, 11471, 11472, 11473, 11474, 11475, 11476, 11477, 11478, 11479, 11480, 11481, 11482, 11483, 11484, 11485, 11486, 11487, 16384, 16385, 16386, 16388, 16389, 16390, 16392, 16393, 16394, 16395, 16400, 16401, 16402, 16404, 16405, 16406, 16408, 16409, 16410, 16411, 16416, 16417, 16418, 16419, 16420, 16421, 16422, 16423, 16424, 16425, 16426, 16427, 16428, 16429, 16430, 16431, 16512, 16513, 16514, 16516, 16517, 16518, 16520, 16521, 16522, 16523, 16528, 16529, 16530, 16532, 16533, 16534, 16536, 16537, 16538, 16539, 16544, 16545, 16546, 16547, 16548, 16549, 16550, 16551, 16552, 16553, 16554, 16555, 16556, 16557, 16558, 16559, 16640, 16641, 16642, 16644, 16645, 16646, 16648, 16649, 16650, 16651, 16656, 16657, 16658, 16660, 16661, 16662, 16664, 16665, 16666, 16667, 16672, 16673, 16674, 16675, 16676, 16677, 16678, 16679, 16680, 16681, 16682, 16683, 16684, 16685, 16686, 16687, 16768, 16770, 16771, 16772, 16774, 16775, 16776, 16777, 16778, 16779, 16784, 16786, 16787, 16788, 16790, 16791, 16792, 16793, 16794, 16795, 16800, 16801, 16802, 16803, 16804, 16805, 16806, 16807, 16808, 16809, 16810, 16811, 16812, 16813, 16814, 16815, 16896, 16897, 16898, 16899, 16900, 16901, 16902, 16903, 16904, 16905, 16906, 16907, 16908, 16909, 16910, 16911, 16912, 16913, 16914, 16915, 16916, 16917, 16918, 16919, 16920, 16921, 16922, 16923, 16924, 16925, 16926, 16927, 16928, 16929, 16930, 16931, 16932, 16933, 16934, 16935, 16936, 16937, 16938, 16939, 16940, 16941, 16942, 16943, 16944, 16945, 16946, 16947, 16948, 16949, 16950, 16951, 16952, 16953, 16954, 16955, 16956, 16957, 16958, 16959, 17024, 17025, 17026, 17027, 17028, 17029, 17030, 17031, 17032, 17033, 17034, 17035, 17036, 17037, 17038, 17039, 17040, 17041, 17042, 17043, 17044, 17045, 17046, 17047, 17048, 17049, 17050, 17051, 17052, 17053, 17054, 17055, 17056, 17057, 17058, 17059, 17060, 17061, 17062, 17063, 17064, 17065, 17066, 17067, 17068, 17069, 17070, 17071, 17072, 17073, 17074, 17075, 17076, 17077, 17078, 17079, 17080, 17081, 17082, 17083, 17084, 17085, 17086, 17087, 18432, 18433, 18434, 18436, 18437, 18438, 18440, 18441, 18442, 18443, 18448, 18450, 18451, 18452, 18454, 18455, 18456, 18457, 18458, 18459, 18464, 18465, 18466, 18467, 18468, 18469, 18470, 18471, 18472, 18473, 18474, 18475, 18476, 18477, 18478, 18479, 18560, 18561, 18562, 18563, 18568, 18569, 18570, 18572, 18573, 18574, 18576, 18577, 18578, 18579, 18584, 18586, 18587, 18588, 18590, 18591, 18592, 18593, 18594, 18595, 18596, 18597, 18598, 18599, 18600, 18601, 18602, 18603, 18604, 18605, 18606, 18607, 18688, 18689, 18690, 18692, 18693, 18694, 18696, 18697, 18698, 18699, 18704, 18706, 18707, 18708, 18710, 18711, 18712, 18713, 18714, 18715, 18720, 18721, 18722, 18723, 18724, 18725, 18726, 18727, 18728, 18729, 18730, 18731, 18732, 18733, 18734, 18735, 18816, 18817, 18818, 18819, 18824, 18826, 18827, 18828, 18830, 18831, 18832, 18833, 18834, 18835, 18840, 18841, 18842, 18844, 18845, 18846, 18848, 18849, 18850, 18851, 18852, 18853, 18854, 18855, 18856, 18857, 18858, 18859, 18860, 18861, 18862, 18863, 18944, 18945, 18946, 18947, 18948, 18949, 18950, 18951, 18952, 18953, 18954, 18955, 18956, 18957, 18958, 18959, 18960, 18961, 18962, 18963, 18964, 18965, 18966, 18967, 18968, 18969, 18970, 18971, 18972, 18973, 18974, 18975, 18976, 18977, 18978, 18979, 18980, 18981, 18982, 18983, 18984, 18985, 18986, 18987, 18988, 18989, 18990, 18991, 18992, 18993, 18994, 18995, 18996, 18997, 18998, 18999, 19000, 19001, 19002, 19003, 19004, 19005, 19006, 19007, 19072, 19073, 19074, 19075, 19076, 19077, 19078, 19079, 19080, 19081, 19082, 19083, 19084, 19085, 19086, 19087, 19088, 19089, 19090, 19091, 19092, 19093, 19094, 19095, 19096, 19097, 19098, 19099, 19100, 19101, 19102, 19103, 19104, 19105, 19106, 19107, 19108, 19109, 19110, 19111, 19112, 19113, 19114, 19115, 19116, 19117, 19118, 19119, 19120, 19121, 19122, 19123, 19124, 19125, 19126, 19127, 19128, 19129, 19130, 19131, 19132, 19133, 19134, 19135, 24576, 24577, 24578, 24580, 24582, 24583, 24584, 24585, 24586, 24587, 24592, 24593, 24594, 24596, 24598, 24599, 24600, 24601, 24602, 24603, 24608, 24609, 24610, 24611, 24612, 24613, 24614, 24615, 24616, 24617, 24618, 24619, 24620, 24621, 24622, 24623, 24704, 24705, 24706, 24707, 24708, 24709, 24710, 24711, 24712, 24713, 24714, 24715, 24716, 24717, 24718, 24719, 24736, 24737, 24738, 24740, 24742, 24743, 24744, 24745, 24746, 24747, 24752, 24753, 24754, 24756, 24758, 24759, 24760, 24761, 24762, 24763, 24832, 24833, 24834, 24836, 24838, 24839, 24840, 24841, 24842, 24843, 24848, 24849, 24850, 24852, 24854, 24855, 24856, 24857, 24858, 24859, 24864, 24865, 24866, 24867, 24868, 24869, 24870, 24871, 24872, 24873, 24874, 24875, 24876, 24877, 24878, 24879, 24960, 24961, 24962, 24963, 24964, 24965, 24966, 24967, 24968, 24969, 24970, 24971, 24972, 24973, 24974, 24975, 24992, 24994, 24995, 24996, 24997, 24998, 25000, 25001, 25002, 25003, 25008, 25010, 25011, 25012, 25013, 25014, 25016, 25017, 25018, 25019, 25088, 25089, 25090, 25091, 25092, 25093, 25094, 25095, 25096, 25097, 25098, 25099, 25100, 25101, 25102, 25103, 25104, 25105, 25106, 25107, 25108, 25109, 25110, 25111, 25112, 25113, 25114, 25115, 25116, 25117, 25118, 25119, 25120, 25121, 25122, 25123, 25124, 25125, 25126, 25127, 25128, 25129, 25130, 25131, 25132, 25133, 25134, 25135, 25136, 25137, 25138, 25139, 25140, 25141, 25142, 25143, 25144, 25145, 25146, 25147, 25148, 25149, 25150, 25151, 25216, 25217, 25218, 25219, 25220, 25221, 25222, 25223, 25224, 25225, 25226, 25227, 25228, 25229, 25230, 25231, 25232, 25233, 25234, 25235, 25236, 25237, 25238, 25239, 25240, 25241, 25242, 25243, 25244, 25245, 25246, 25247, 25248, 25249, 25250, 25251, 25252, 25253, 25254, 25255, 25256, 25257, 25258, 25259, 25260, 25261, 25262, 25263, 25264, 25265, 25266, 25267, 25268, 25269, 25270, 25271, 25272, 25273, 25274, 25275, 25276, 25277, 25278, 25279, 26624, 26625, 26626, 26627, 26628, 26629, 26630, 26631, 26632, 26633, 26634, 26635, 26636, 26637, 26638, 26639, 26640, 26641, 26642, 26643, 26644, 26645, 26646, 26647, 26648, 26649, 26650, 26651, 26652, 26653, 26654, 26655, 26656, 26657, 26658, 26659, 26660, 26661, 26662, 26663, 26664, 26665, 26666, 26667, 26668, 26669, 26670, 26671, 26672, 26673, 26674, 26675, 26676, 26677, 26678, 26679, 26680, 26681, 26682, 26683, 26684, 26685, 26686, 26687, 26752, 26753, 26754, 26755, 26756, 26757, 26758, 26759, 26760, 26761, 26762, 26763, 26764, 26765, 26766, 26767, 26768, 26769, 26770, 26771, 26772, 26773, 26774, 26775, 26776, 26777, 26778, 26779, 26780, 26781, 26782, 26783, 26784, 26785, 26786, 26787, 26788, 26789, 26790, 26791, 26792, 26793, 26794, 26795, 26796, 26797, 26798, 26799, 26800, 26801, 26802, 26803, 26804, 26805, 26806, 26807, 26808, 26809, 26810, 26811, 26812, 26813, 26814, 26815, 27136, 27137, 27138, 27140, 27142, 27143, 27144, 27145, 27146, 27147, 27152, 27154, 27155, 27156, 27157, 27158, 27160, 27161, 27162, 27163, 27168, 27169, 27170, 27171, 27172, 27173, 27174, 27175, 27176, 27177, 27178, 27179, 27180, 27181, 27182, 27183, 27264, 27265, 27266, 27267, 27268, 27269, 27270, 27271, 27272, 27273, 27274, 27275, 27276, 27277, 27278, 27279, 27296, 27297, 27298, 27299, 27304, 27306, 27307, 27308, 27309, 27310, 27312, 27313, 27314, 27315, 27320, 27321, 27322, 27324, 27326, 27327, 27392, 27393, 27394, 27396, 27398, 27399, 27400, 27401, 27402, 27403, 27408, 27410, 27411, 27412, 27413, 27414, 27416, 27417, 27418, 27419, 27424, 27425, 27426, 27427, 27428, 27429, 27430, 27431, 27432, 27433, 27434, 27435, 27436, 27437, 27438, 27439, 27520, 27521, 27522, 27523, 27524, 27525, 27526, 27527, 27528, 27529, 27530, 27531, 27532, 27533, 27534, 27535, 27552, 27553, 27554, 27555, 27560, 27561, 27562, 27564, 27566, 27567, 27568, 27569, 27570, 27571, 27576, 27578, 27579, 27580, 27581, 27582, 32768, 32769, 32770, 32771, 32772, 32773, 32774, 32775, 32776, 32777, 32778, 32779, 32780, 32781, 32782, 32783, 32784, 32785, 32786, 32787, 32788, 32789, 32790, 32791, 32792, 32793, 32794, 32795, 32796, 32797, 32798, 32799, 32800, 32801, 32802, 32803, 32804, 32805, 32806, 32807, 32808, 32809, 32810, 32811, 32812, 32813, 32814, 32815, 32816, 32817, 32818, 32819, 32820, 32821, 32822, 32823, 32824, 32825, 32826, 32827, 32828, 32829, 32830, 32831, 32832, 32833, 32834, 32835, 32836, 32837, 32838, 32839, 32840, 32841, 32842, 32843, 32844, 32845, 32846, 32847, 32848, 32849, 32850, 32851, 32852, 32853, 32854, 32855, 32856, 32857, 32858, 32859, 32860, 32861, 32862, 32863, 32864, 32865, 32866, 32867, 32868, 32869, 32870, 32871, 32872, 32873, 32874, 32875, 32876, 32877, 32878, 32879, 32880, 32881, 32882, 32883, 32884, 32885, 32886, 32887, 32888, 32889, 32890, 32891, 32892, 32893, 32894, 32895, 33024, 33025, 33026, 33027, 33028, 33029, 33030, 33031, 33032, 33033, 33034, 33035, 33036, 33037, 33038, 33039, 33040, 33041, 33042, 33043, 33044, 33045, 33046, 33047, 33048, 33049, 33050, 33051, 33052, 33053, 33054, 33055, 33056, 33057, 33058, 33059, 33060, 33061, 33062, 33063, 33064, 33065, 33066, 33067, 33068, 33069, 33070, 33071, 33072, 33073, 33074, 33075, 33076, 33077, 33078, 33079, 33080, 33081, 33082, 33083, 33084, 33085, 33086, 33087, 33088, 33089, 33090, 33091, 33092, 33093, 33094, 33095, 33096, 33097, 33098, 33099, 33100, 33101, 33102, 33103, 33104, 33105, 33106, 33107, 33108, 33109, 33110, 33111, 33112, 33113, 33114, 33115, 33116, 33117, 33118, 33119, 33120, 33121, 33122, 33123, 33124, 33125, 33126, 33127, 33128, 33129, 33130, 33131, 33132, 33133, 33134, 33135, 33136, 33137, 33138, 33139, 33140, 33141, 33142, 33143, 33144, 33145, 33146, 33147, 33148, 33149, 33150, 33151, 33280, 33281, 33282, 33283, 33284, 33285, 33286, 33287, 33288, 33289, 33290, 33291, 33292, 33293, 33294, 33295, 33296, 33297, 33298, 33299, 33300, 33301, 33302, 33303, 33304, 33305, 33306, 33307, 33308, 33309, 33310, 33311, 33312, 33313, 33314, 33315, 33316, 33317, 33318, 33319, 33320, 33321, 33322, 33323, 33324, 33325, 33326, 33327, 33328, 33329, 33330, 33331, 33332, 33333, 33334, 33335, 33336, 33337, 33338, 33339, 33340, 33341, 33342, 33343, 33344, 33345, 33346, 33347, 33348, 33349, 33350, 33351, 33352, 33353, 33354, 33355, 33356, 33357, 33358, 33359, 33360, 33361, 33362, 33363, 33364, 33365, 33366, 33367, 33368, 33369, 33370, 33371, 33372, 33373, 33374, 33375, 33376, 33377, 33378, 33379, 33380, 33381, 33382, 33383, 33384, 33385, 33386, 33387, 33388, 33389, 33390, 33391, 33392, 33393, 33394, 33395, 33396, 33397, 33398, 33399, 33400, 33401, 33402, 33403, 33404, 33405, 33406, 33407, 33536, 33537, 33538, 33539, 33540, 33541, 33542, 33543, 33544, 33545, 33546, 33547, 33548, 33549, 33550, 33551, 33552, 33553, 33554, 33555, 33556, 33557, 33558, 33559, 33560, 33561, 33562, 33563, 33564, 33565, 33566, 33567, 33568, 33569, 33570, 33571, 33572, 33573, 33574, 33575, 33576, 33577, 33578, 33579, 33580, 33581, 33582, 33583, 33584, 33585, 33586, 33587, 33588, 33589, 33590, 33591, 33592, 33593, 33594, 33595, 33596, 33597, 33598, 33599, 33600, 33601, 33602, 33603, 33604, 33605, 33606, 33607, 33608, 33609, 33610, 33611, 33612, 33613, 33614, 33615, 33616, 33617, 33618, 33619, 33620, 33621, 33622, 33623, 33624, 33625, 33626, 33627, 33628, 33629, 33630, 33631, 33632, 33633, 33634, 33635, 33636, 33637, 33638, 33639, 33640, 33641, 33642, 33643, 33644, 33645, 33646, 33647, 33648, 33649, 33650, 33651, 33652, 33653, 33654, 33655, 33656, 33657, 33658, 33659, 33660, 33661, 33662, 33663, 33792, 33793, 33794, 33795, 33796, 33797, 33798, 33799, 33800, 33801, 33802, 33803, 33804, 33805, 33806, 33807, 33808, 33809, 33810, 33811, 33812, 33813, 33814, 33815, 33816, 33817, 33818, 33819, 33820, 33821, 33822, 33823, 33824, 33825, 33826, 33827, 33828, 33829, 33830, 33831, 33832, 33833, 33834, 33835, 33836, 33837, 33838, 33839, 33840, 33841, 33842, 33843, 33844, 33845, 33846, 33847, 33848, 33849, 33850, 33851, 33852, 33853, 33854, 33855, 33856, 33857, 33858, 33859, 33860, 33861, 33862, 33863, 33864, 33865, 33866, 33867, 33868, 33869, 33870, 33871, 33872, 33873, 33874, 33875, 33876, 33877, 33878, 33879, 33880, 33881, 33882, 33883, 33884, 33885, 33886, 33887, 33888, 33889, 33890, 33891, 33892, 33893, 33894, 33895, 33896, 33897, 33898, 33899, 33900, 33901, 33902, 33903, 33904, 33905, 33906, 33907, 33908, 33909, 33910, 33911, 33912, 33913, 33914, 33915, 33916, 33917, 33918, 33919, 34048, 34049, 34050, 34051, 34052, 34053, 34054, 34055, 34056, 34057, 34058, 34059, 34060, 34061, 34062, 34063, 34064, 34065, 34066, 34067, 34068, 34069, 34070, 34071, 34072, 34073, 34074, 34075, 34076, 34077, 34078, 34079, 34080, 34081, 34082, 34083, 34084, 34085, 34086, 34087, 34088, 34089, 34090, 34091, 34092, 34093, 34094, 34095, 34096, 34097, 34098, 34099, 34100, 34101, 34102, 34103, 34104, 34105, 34106, 34107, 34108, 34109, 34110, 34111, 34112, 34113, 34114, 34115, 34116, 34117, 34118, 34119, 34120, 34121, 34122, 34123, 34124, 34125, 34126, 34127, 34128, 34129, 34130, 34131, 34132, 34133, 34134, 34135, 34136, 34137, 34138, 34139, 34140, 34141, 34142, 34143, 34144, 34145, 34146, 34147, 34148, 34149, 34150, 34151, 34152, 34153, 34154, 34155, 34156, 34157, 34158, 34159, 34160, 34161, 34162, 34163, 34164, 34165, 34166, 34167, 34168, 34169, 34170, 34171, 34172, 34173, 34174, 34175, 34304, 34305, 34306, 34307, 34308, 34309, 34310, 34311, 34312, 34313, 34314, 34315, 34316, 34317, 34318, 34319, 34320, 34321, 34322, 34323, 34324, 34325, 34326, 34327, 34328, 34329, 34330, 34331, 34332, 34333, 34334, 34335, 34336, 34337, 34338, 34339, 34340, 34341, 34342, 34343, 34344, 34345, 34346, 34347, 34348, 34349, 34350, 34351, 34352, 34353, 34354, 34355, 34356, 34357, 34358, 34359, 34360, 34361, 34362, 34363, 34364, 34365, 34366, 34367, 34368, 34369, 34370, 34371, 34372, 34373, 34374, 34375, 34376, 34377, 34378, 34379, 34380, 34381, 34382, 34383, 34384, 34385, 34386, 34387, 34388, 34389, 34390, 34391, 34392, 34393, 34394, 34395, 34396, 34397, 34398, 34399, 34400, 34401, 34402, 34403, 34404, 34405, 34406, 34407, 34408, 34409, 34410, 34411, 34412, 34413, 34414, 34415, 34416, 34417, 34418, 34419, 34420, 34421, 34422, 34423, 34424, 34425, 34426, 34427, 34428, 34429, 34430, 34431, 34560, 34561, 34562, 34563, 34564, 34565, 34566, 34567, 34568, 34569, 34570, 34571, 34572, 34573, 34574, 34575, 34576, 34577, 34578, 34579, 34580, 34581, 34582, 34583, 34584, 34585, 34586, 34587, 34588, 34589, 34590, 34591, 34592, 34593, 34594, 34595, 34596, 34597, 34598, 34599, 34600, 34601, 34602, 34603, 34604, 34605, 34606, 34607, 34608, 34609, 34610, 34611, 34612, 34613, 34614, 34615, 34616, 34617, 34618, 34619, 34620, 34621, 34622, 34623, 34624, 34625, 34626, 34627, 34628, 34629, 34630, 34631, 34632, 34633, 34634, 34635, 34636, 34637, 34638, 34639, 34640, 34641, 34642, 34643, 34644, 34645, 34646, 34647, 34648, 34649, 34650, 34651, 34652, 34653, 34654, 34655, 34656, 34657, 34658, 34659, 34660, 34661, 34662, 34663, 34664, 34665, 34666, 34667, 34668, 34669, 34670, 34671, 34672, 34673, 34674, 34675, 34676, 34677, 34678, 34679, 34680, 34681, 34682, 34683, 34684, 34685, 34686, 34687, 36864, 36865, 36866, 36867, 36868, 36869, 36870, 36871, 36872, 36873, 36874, 36875, 36876, 36877, 36878, 36879, 36880, 36881, 36882, 36883, 36884, 36885, 36886, 36887, 36888, 36889, 36890, 36891, 36892, 36893, 36894, 36895, 36896, 36897, 36898, 36899, 36900, 36901, 36902, 36903, 36904, 36905, 36906, 36907, 36908, 36909, 36910, 36911, 36912, 36913, 36914, 36915, 36916, 36917, 36918, 36919, 36920, 36921, 36922, 36923, 36924, 36925, 36926, 36927, 36928, 36929, 36930, 36931, 36932, 36933, 36934, 36935, 36936, 36937, 36938, 36939, 36940, 36941, 36942, 36943, 36944, 36945, 36946, 36947, 36948, 36949, 36950, 36951, 36952, 36953, 36954, 36955, 36956, 36957, 36958, 36959, 36960, 36961, 36962, 36963, 36964, 36965, 36966, 36967, 36968, 36969, 36970, 36971, 36972, 36973, 36974, 36975, 36976, 36977, 36978, 36979, 36980, 36981, 36982, 36983, 36984, 36985, 36986, 36987, 36988, 36989, 36990, 36991, 37120, 37121, 37122, 37123, 37124, 37125, 37126, 37127, 37128, 37129, 37130, 37131, 37132, 37133, 37134, 37135, 37136, 37137, 37138, 37139, 37140, 37141, 37142, 37143, 37144, 37145, 37146, 37147, 37148, 37149, 37150, 37151, 37152, 37153, 37154, 37155, 37156, 37157, 37158, 37159, 37160, 37161, 37162, 37163, 37164, 37165, 37166, 37167, 37168, 37169, 37170, 37171, 37172, 37173, 37174, 37175, 37176, 37177, 37178, 37179, 37180, 37181, 37182, 37183, 37184, 37185, 37186, 37187, 37188, 37189, 37190, 37191, 37192, 37193, 37194, 37195, 37196, 37197, 37198, 37199, 37200, 37201, 37202, 37203, 37204, 37205, 37206, 37207, 37208, 37209, 37210, 37211, 37212, 37213, 37214, 37215, 37216, 37217, 37218, 37219, 37220, 37221, 37222, 37223, 37224, 37225, 37226, 37227, 37228, 37229, 37230, 37231, 37232, 37233, 37234, 37235, 37236, 37237, 37238, 37239, 37240, 37241, 37242, 37243, 37244, 37245, 37246, 37247, 37376, 37377, 37378, 37379, 37380, 37381, 37382, 37383, 37384, 37385, 37386, 37387, 37388, 37389, 37390, 37391, 37392, 37393, 37394, 37395, 37396, 37397, 37398, 37399, 37400, 37401, 37402, 37403, 37404, 37405, 37406, 37407, 37408, 37409, 37410, 37411, 37412, 37413, 37414, 37415, 37416, 37417, 37418, 37419, 37420, 37421, 37422, 37423, 37424, 37425, 37426, 37427, 37428, 37429, 37430, 37431, 37432, 37433, 37434, 37435, 37436, 37437, 37438, 37439, 37440, 37441, 37442, 37443, 37444, 37445, 37446, 37447, 37448, 37449, 37450, 37451, 37452, 37453, 37454, 37455, 37456, 37457, 37458, 37459, 37460, 37461, 37462, 37463, 37464, 37465, 37466, 37467, 37468, 37469, 37470, 37471, 37472, 37473, 37474, 37475, 37476, 37477, 37478, 37479, 37480, 37481, 37482, 37483, 37484, 37485, 37486, 37487, 37488, 37489, 37490, 37491, 37492, 37493, 37494, 37495, 37496, 37497, 37498, 37499, 37500, 37501, 37502, 37503, 37632, 37633, 37634, 37635, 37636, 37637, 37638, 37639, 37640, 37641, 37642, 37643, 37644, 37645, 37646, 37647, 37648, 37649, 37650, 37651, 37652, 37653, 37654, 37655, 37656, 37657, 37658, 37659, 37660, 37661, 37662, 37663, 37664, 37665, 37666, 37667, 37668, 37669, 37670, 37671, 37672, 37673, 37674, 37675, 37676, 37677, 37678, 37679, 37680, 37681, 37682, 37683, 37684, 37685, 37686, 37687, 37688, 37689, 37690, 37691, 37692, 37693, 37694, 37695, 37696, 37697, 37698, 37699, 37700, 37701, 37702, 37703, 37704, 37705, 37706, 37707, 37708, 37709, 37710, 37711, 37712, 37713, 37714, 37715, 37716, 37717, 37718, 37719, 37720, 37721, 37722, 37723, 37724, 37725, 37726, 37727, 37728, 37729, 37730, 37731, 37732, 37733, 37734, 37735, 37736, 37737, 37738, 37739, 37740, 37741, 37742, 37743, 37744, 37745, 37746, 37747, 37748, 37749, 37750, 37751, 37752, 37753, 37754, 37755, 37756, 37757, 37758, 37759, 37888, 37889, 37890, 37891, 37892, 37893, 37894, 37895, 37896, 37897, 37898, 37899, 37900, 37901, 37902, 37903, 37904, 37905, 37906, 37907, 37908, 37909, 37910, 37911, 37912, 37913, 37914, 37915, 37916, 37917, 37918, 37919, 37920, 37921, 37922, 37923, 37924, 37925, 37926, 37927, 37928, 37929, 37930, 37931, 37932, 37933, 37934, 37935, 37936, 37937, 37938, 37939, 37940, 37941, 37942, 37943, 37944, 37945, 37946, 37947, 37948, 37949, 37950, 37951, 37952, 37953, 37954, 37955, 37956, 37957, 37958, 37959, 37960, 37961, 37962, 37963, 37964, 37965, 37966, 37967, 37968, 37969, 37970, 37971, 37972, 37973, 37974, 37975, 37976, 37977, 37978, 37979, 37980, 37981, 37982, 37983, 37984, 37985, 37986, 37987, 37988, 37989, 37990, 37991, 37992, 37993, 37994, 37995, 37996, 37997, 37998, 37999, 38000, 38001, 38002, 38003, 38004, 38005, 38006, 38007, 38008, 38009, 38010, 38011, 38012, 38013, 38014, 38015, 38144, 38145, 38146, 38147, 38148, 38149, 38150, 38151, 38152, 38153, 38154, 38155, 38156, 38157, 38158, 38159, 38160, 38161, 38162, 38163, 38164, 38165, 38166, 38167, 38168, 38169, 38170, 38171, 38172, 38173, 38174, 38175, 38176, 38177, 38178, 38179, 38180, 38181, 38182, 38183, 38184, 38185, 38186, 38187, 38188, 38189, 38190, 38191, 38192, 38193, 38194, 38195, 38196, 38197, 38198, 38199, 38200, 38201, 38202, 38203, 38204, 38205, 38206, 38207, 38208, 38209, 38210, 38211, 38212, 38213, 38214, 38215, 38216, 38217, 38218, 38219, 38220, 38221, 38222, 38223, 38224, 38225, 38226, 38227, 38228, 38229, 38230, 38231, 38232, 38233, 38234, 38235, 38236, 38237, 38238, 38239, 38240, 38241, 38242, 38243, 38244, 38245, 38246, 38247, 38248, 38249, 38250, 38251, 38252, 38253, 38254, 38255, 38256, 38257, 38258, 38259, 38260, 38261, 38262, 38263, 38264, 38265, 38266, 38267, 38268, 38269, 38270, 38271, 38400, 38401, 38402, 38403, 38404, 38405, 38406, 38407, 38408, 38409, 38410, 38411, 38412, 38413, 38414, 38415, 38416, 38417, 38418, 38419, 38420, 38421, 38422, 38423, 38424, 38425, 38426, 38427, 38428, 38429, 38430, 38431, 38432, 38433, 38434, 38435, 38436, 38437, 38438, 38439, 38440, 38441, 38442, 38443, 38444, 38445, 38446, 38447, 38448, 38449, 38450, 38451, 38452, 38453, 38454, 38455, 38456, 38457, 38458, 38459, 38460, 38461, 38462, 38463, 38464, 38465, 38466, 38467, 38468, 38469, 38470, 38471, 38472, 38473, 38474, 38475, 38476, 38477, 38478, 38479, 38480, 38481, 38482, 38483, 38484, 38485, 38486, 38487, 38488, 38489, 38490, 38491, 38492, 38493, 38494, 38495, 38496, 38497, 38498, 38499, 38500, 38501, 38502, 38503, 38504, 38505, 38506, 38507, 38508, 38509, 38510, 38511, 38512, 38513, 38514, 38515, 38516, 38517, 38518, 38519, 38520, 38521, 38522, 38523, 38524, 38525, 38526, 38527, 38656, 38657, 38658, 38659, 38660, 38661, 38662, 38663, 38664, 38665, 38666, 38667, 38668, 38669, 38670, 38671, 38672, 38673, 38674, 38675, 38676, 38677, 38678, 38679, 38680, 38681, 38682, 38683, 38684, 38685, 38686, 38687, 38688, 38689, 38690, 38691, 38692, 38693, 38694, 38695, 38696, 38697, 38698, 38699, 38700, 38701, 38702, 38703, 38704, 38705, 38706, 38707, 38708, 38709, 38710, 38711, 38712, 38713, 38714, 38715, 38716, 38717, 38718, 38719, 38720, 38721, 38722, 38723, 38724, 38725, 38726, 38727, 38728, 38729, 38730, 38731, 38732, 38733, 38734, 38735, 38736, 38737, 38738, 38739, 38740, 38741, 38742, 38743, 38744, 38745, 38746, 38747, 38748, 38749, 38750, 38751, 38752, 38753, 38754, 38755, 38756, 38757, 38758, 38759, 38760, 38761, 38762, 38763, 38764, 38765, 38766, 38767, 38768, 38769, 38770, 38771, 38772, 38773, 38774, 38775, 38776, 38777, 38778, 38779, 38780, 38781, 38782, 38783 |
A227725 $T(n,k)$ is the number of $n$-ary families of size $2^{k}$. A227724 $T(n,k)$ is the number of balanced $n$-ary families of size $2^{k}$. A054724 $T(n,w)$ is the number of $n$-ary families with weight $w$. See here.

## blunt and sharp

Sharp families always have the maximal size. Each member of sharp family has a unique consul, while all members of a blunt family have the same consul. All sharp families belong to the same tribe. The tribe of a blunt family is denoted by the binary weight of the consul.
It is easy to calculate a family representative of a sharp BF (a male to be precise), namely the one with consul 0.
There are many bijections between blunt and sharp Boolean functions. It would be practical to have one, that assigns all members of a blunt family to members of the same sharp family. So one sharp family would correspond to a set of blunt families. That would be nice to have, but may not exist.
An important fact (visible in the table of sequences above) is that the number of blunt families is equal to the number of super-families. The numbers of sharp and introverted (self-complementary) families always sum up to the number of blunt families (= the number of super-families).
Arity 1 is a special case, because the one sharp and the one introverted family are the same. Apart from that, no sharp familiy is introverted.
sharp to extroverted blunt :
introverted :

## super-clans

The following table shows the 46 3-ary families within the 14 super-clans. That means, each family is shown in its clan, and together with its complement. In each matrix a family has a distinct color. Complements have the same base color (RGB or beige). Clans have the same shade (light or dark). (The number of families in a super-clan is 1, 2, 3 or 6.)
tables of super-clans :
sharp :
| f/c | weight | quaestor weight | rep. |
| 1 | 1, 7 | 1 | 128 128 Ж 128 |
| 1 | 3, 5 | 3 | 150 22 Ж 150 |
| 3 | 3, 5 | 3 | 130 42 Ж 130 |
| 3 | 3, 5 | 1 | 134 230 Ж 134 |
blunt extroverted :
| f/c | family size | weight | consul weight | quaestor weight | rep. |
| 1 | 1 | 0, 8 | 0 | 0 | 0 0 Ж 0 |
| 1 | 4 | 2, 6 | 3 | 0 | 106 66 Ж 106 |
| 3 | 4 | 2, 6 | 2 | 2 | 40 40 Ж 40 |
| 3 | 4 | 2, 6 | 1 | 2 | 8 136 Ж 8 |
blunt introverted :
| f/c | family size | consul weight | quaestor weight | 🤥 | rep. |
| 1 | 2 | 0 | 4 | honest | 22 150 Ж 22 |
| 3 | 2 | 0 | 4 | honest | 2 170 Ж 2 |
| 3 | 2 | 0 | 0 | honest | 6 102 Ж 6 |
| 1 | 8 | 3 | 4 | dishonest | 104 232 Ж 104 |
| 3 | 8 | 1 | 2 | dishonest | 24 120 Ж 24 |
| 3 | 8 | 2 | 2 | dishonest | 44 228 Ж 44 |

## super-families

The following table shows the 46 3-ary families within the 30 super-families. That means, each family is shown together with its complement. An important property (that links the 3-ary to 2-ary families) is the village – seen as columns in the matrices of Zhegalkin indices. Blunt families have a consul and a solidity. (Sharp families have four solid and four fluid members.)
tables of super-families :
sharp :
| weight | quaestor weight | reps. | reps. | truth tables | Zhegalkin indices | village | village | village | village |
| weight | quaestor weight | sc | sf | truth tables | Zhegalkin indices | size | | reverse | rep. |
| 1, 7 | 1 | Ж 128 | 128 128 Ж 128 | | | 4 | {1, 3, 5, 15} | T {8, 4, 2, 1} Z {8, 12, 10, 15} | 128 8 Ж 8 |
| 3, 5 | 3 | Ж 130 | 130 42 Ж 130 | | | 4 | {1, 3, 5, 15} | T {8, 4, 2, 1} Z {8, 12, 10, 15} | 130 8 Ж 8 |
| 3, 5 | 3 | Ж 130 | 132 76 Ж 132 | | | 4 | {1, 3, 5, 15} | T {8, 4, 2, 1} Z {8, 12, 10, 15} | 132 8 Ж 8 |
| 3, 5 | 1 | Ж 134 | 134 230 Ж 134 | | | 4 | {1, 3, 5, 15} | T {8, 4, 2, 1} Z {8, 12, 10, 15} | 134 8 Ж 8 |
| 3, 5 | 3 | Ж 130 | 144 112 Ж 144 | | | 4 | {7, 9, 11, 13} | T {14, 7, 11, 13} Z {14, 9, 13, 11} | 144 7 Ж 9 |
| 3, 5 | 1 | Ж 134 | 146 218 Ж 146 | | | 4 | {7, 9, 11, 13} | T {14, 7, 11, 13} Z {14, 9, 13, 11} | 146 7 Ж 9 |
| 3, 5 | 1 | Ж 134 | 148 188 Ж 148 | | | 4 | {7, 9, 11, 13} | T {14, 7, 11, 13} Z {14, 9, 13, 11} | 148 7 Ж 9 |
| 3, 5 | 3 | Ж 150 | 150 22 Ж 150 | | | 4 | {7, 9, 11, 13} | T {14, 7, 11, 13} Z {14, 9, 13, 11} | 150 7 Ж 9 |
blunt extroverted :
| size | weight | consul | consul | 🧊 | quaestor weight | reps. | reps. | truth tables | Zhegalkin indices | village | village | village | village |
| size | weight | | | 🧊 | quaestor weight | sc | sf | truth tables | Zhegalkin indices | size | | reverse | rep. |
| 1 | 0, 8 | 0 | 0 | fluid | 0 | Ж 0 | 0 0 Ж 0 | | | 1 | {0} | T {0} Z {0} | 0 0 Ж 0 |
| 4 | 2, 6 | 1 | 4 | solid | 2 | Ж 8 | 8 136 Ж 8 | | | 1 | {0} | T {0} Z {0} | 8 0 Ж 0 |
| 4 | 2, 6 | 1 | 2 | solid | 2 | Ж 8 | 32 160 Ж 32 | | | 2 | {4, 12} | T {10, 5} Z {2, 3} | 32 10 Ж 2 |
| 4 | 2, 6 | 2 | 6 | fluid | 2 | Ж 40 | 40 40 Ж 40 | | | 2 | {4, 12} | T {10, 5} Z {2, 3} | 40 10 Ж 2 |
| 4 | 2, 6 | 1 | 1 | fluid | 2 | Ж 8 | 64 192 Ж 64 | | | 2 | {2, 10} | T {12, 3} Z {4, 5} | 64 12 Ж 4 |
| 4 | 2, 6 | 2 | 5 | solid | 2 | Ж 40 | 72 72 Ж 72 | | | 2 | {2, 10} | T {12, 3} Z {4, 5} | 72 12 Ж 4 |
| 4 | 2, 6 | 2 | 3 | solid | 2 | Ж 40 | 96 96 Ж 96 | | | 2 | {6, 14} | T {6, 9} Z {6, 7} | 96 6 Ж 6 |
| 4 | 2, 6 | 3 | 7 | fluid | 0 | Ж 106 | 106 66 Ж 106 | | | 2 | {6, 14} | T {6, 9} Z {6, 7} | 106 6 Ж 6 |
blunt introverted :
| size | consul | consul | 🧊 | 🤥 | quaestor weight | reps. | reps. | truth tables | Zhegalkin indices | village | village | village | village |
| size | | | 🧊 | 🤥 | quaestor weight | sc | sf | truth tables | Zhegalkin indices | size | | reverse | rep. |
| 2 | 0 | 0 | fluid | honest | 4 | Ж 2 | 2 170 Ж 2 | | | 1 | {0} | T {0} Z {0} | 2 0 Ж 0 |
| 2 | 0 | 0 | fluid | honest | 4 | Ж 2 | 4 204 Ж 4 | | | 1 | {0} | T {0} Z {0} | 4 0 Ж 0 |
| 2 | 0 | 0 | fluid | honest | 0 | Ж 6 | 6 102 Ж 6 | | | 1 | {0} | T {0} Z {0} | 6 0 Ж 0 |
| 2 | 0 | 0 | fluid | honest | 4 | Ж 2 | 16 240 Ж 16 | | | 1 | {8} | T {15} Z {1} | 16 15 Ж 1 |
| 2 | 0 | 0 | fluid | honest | 0 | Ж 6 | 18 90 Ж 18 | | | 1 | {8} | T {15} Z {1} | 18 15 Ж 1 |
| 2 | 0 | 0 | fluid | honest | 0 | Ж 6 | 20 60 Ж 20 | | | 1 | {8} | T {15} Z {1} | 20 15 Ж 1 |
| 2 | 0 | 0 | fluid | honest | 4 | Ж 22 | 22 150 Ж 22 | | | 1 | {8} | T {15} Z {1} | 22 15 Ж 1 |
| 8 | 1 | 4 | solid | dishonest | 2 | Ж 24 | 24 120 Ж 24 | | | 1 | {8} | T {15} Z {1} | 24 15 Ж 1 |
| 8 | 1 | 2 | solid | dishonest | 2 | Ж 24 | 36 108 Ж 36 | | | 2 | {4, 12} | T {10, 5} Z {2, 3} | 36 10 Ж 2 |
| 8 | 2 | 6 | fluid | dishonest | 2 | Ж 44 | 44 228 Ж 44 | | | 2 | {4, 12} | T {10, 5} Z {2, 3} | 44 10 Ж 2 |
| 8 | 1 | 1 | fluid | dishonest | 2 | Ж 24 | 66 106 Ж 66 | | | 2 | {2, 10} | T {12, 3} Z {4, 5} | 66 12 Ж 4 |
| 8 | 2 | 5 | solid | dishonest | 2 | Ж 44 | 74 226 Ж 74 | | | 2 | {2, 10} | T {12, 3} Z {4, 5} | 74 12 Ж 4 |
| 8 | 2 | 3 | solid | dishonest | 2 | Ж 44 | 98 202 Ж 98 | | | 2 | {6, 14} | T {6, 9} Z {6, 7} | 98 6 Ж 6 |
| 8 | 3 | 7 | fluid | dishonest | 4 | Ж 104 | 104 232 Ж 104 | | | 2 | {6, 14} | T {6, 9} Z {6, 7} | 104 6 Ж 6 |

## misc.

3-ary partitions: family (46), reverse family (46), super family (30), ultra family (18), family size (4), quaestor weight (5), tribe (5), is sharp (2)
* c:Category:3-ary truth tables in octeract matrix; ultra-families
* c:Category:3-ary Boolean functions in octeract matrix; super-clans
* c:Category:3-ary Boolean functions in octeract matrix; reverse super-clans
* c:Category:3-ary Boolean functions; small equivalence classes; cubes
* c:Category:Walsh spectra of 3-ary Boolean functions; families
* c:Category:Family to senior nobles to prefects (image set)