Boolf prop/3-ary/burden


The burden is the pair of truth table weight and Zhegalkin weight.
(The former is actually a fraction, but can be shown as an integer for a given arity.)
Number of blocks: 38 Integer partition: 8⋅1 + 14⋅3 + 8⋅9 + 4⋅12 + 2⋅20 + 2⋅23
| # | weight pair | block |
|---|---|---|
| 1 | (0, 0) | [0]
|
| 1 | (1, 8) | [1]
|
| 3 | (1, 4) | [2, 4, 16]
|
| 9 | (2, 4) | [3, 5, 6, 17, 18, 20, 24, 36, 66]
|
| 20 | (3, 4) | [7, 19, 21, 22, 25, 26, 28, 37, 38, 44, 52, 56, 67, 70, 74, 82, 88, 98, 100, 104]
|
| 3 | (1, 2) | [8, 32, 64]
|
| 3 | (2, 6) | [9, 33, 65]
|
| 9 | (2, 2) | [10, 12, 34, 40, 48, 68, 72, 80, 96]
|
| 12 | (3, 6) | [11, 13, 14, 35, 41, 49, 50, 69, 73, 81, 84, 97]
|
| 9 | (4, 2) | [15, 51, 60, 85, 90, 102, 106, 108, 120]
|
| 23 | (4, 4) | [23, 27, 29, 30, 39, 45, 46, 53, 54, 57, 58, 71, 75, 78, 83, 86, 89, 92, 99, 101, 105, 114, 116]
|
| 12 | (5, 4) | [31, 47, 55, 59, 79, 87, 93, 110, 115, 117, 122, 124]
|
| 3 | (3, 2) | [42, 76, 112]
|
| 3 | (4, 6) | [43, 77, 113]
|
| 9 | (5, 6) | [61, 62, 91, 94, 103, 107, 109, 118, 121]
|
| 3 | (6, 2) | [63, 95, 119]
|
| 3 | (6, 4) | [111, 123, 125]
|
| 1 | (6, 6) | [126]
|
| 1 | (7, 2) | [127]
|
| 1 | (1, 1) | [128]
|
| 1 | (2, 7) | [129]
|
| 3 | (2, 3) | [130, 132, 144]
|
| 9 | (3, 5) | [131, 133, 134, 145, 146, 148, 152, 164, 194]
|
| 20 | (4, 3) | [135, 147, 149, 150, 153, 154, 156, 165, 166, 172, 180, 184, 195, 198, 202, 210, 216, 226, 228, 232]
|
| 3 | (2, 1) | [136, 160, 192]
|
| 3 | (3, 7) | [137, 161, 193]
|
| 9 | (3, 3) | [138, 140, 162, 168, 176, 196, 200, 208, 224]
|
| 12 | (4, 5) | [139, 141, 142, 163, 169, 177, 178, 197, 201, 209, 212, 225]
|
| 9 | (5, 3) | [143, 179, 188, 213, 218, 230, 234, 236, 248]
|
| 23 | (5, 5) | [151, 155, 157, 158, 167, 173, 174, 181, 182, 185, 186, 199, 203, 206, 211, 214, 217, 220, 227, 229, 233, 242, 244]
|
| 12 | (6, 3) | [159, 175, 183, 187, 207, 215, 221, 238, 243, 245, 250, 252]
|
| 3 | (4, 1) | [170, 204, 240]
|
| 3 | (5, 7) | [171, 205, 241]
|
| 9 | (6, 5) | [189, 190, 219, 222, 231, 235, 237, 246, 249]
|
| 3 | (7, 3) | [191, 223, 247]
|
| 3 | (7, 5) | [239, 251, 253]
|
| 1 | (7, 7) | [254]
|
| 1 | (8, 1) | [255]
|





































