Re: Cactus Rules
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CR. Note 21
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Table 17 gives another way of writing the "paisley propositions"
that makes their symmetry class more manifest. The venn diagram
that follows the Table may provide an idea of why I chose to dub
them that, at least, until I can think up a Greek or Latin label.
Table 17. Paisley Propositions
o---------o------------o-----------------o------------------------------o
| L_1 | L_2 | L_3 | L_4 |
| | | | |
| Decimal | Binary | Vector | Cactus |
o---------o------------o-----------------o------------------------------o
| | p : 1 1 1 1 0 0 0 0 | |
| | q : 1 1 0 0 1 1 0 0 | |
| | r : 1 0 1 0 1 0 1 0 | |
o---------o------------o-----------------o------------------------------o
| | | | |
| q_216 | q_11011000 | 1 1 0 1 1 0 0 0 | p + pq + pqr + (p, q, r) |
| | | | |
| q_184 | q_10111000 | 1 0 1 1 1 0 0 0 | p + pr + pqr + (p, q, r) |
| | | | |
| q_228 | q_11100100 | 1 1 1 0 0 1 0 0 | q + pq + pqr + (p, q, r) |
| | | | |
| q_172 | q_10101100 | 1 0 1 0 1 1 0 0 | q + qr + pqr + (p, q, r) |
| | | | |
| q_226 | q_11100010 | 1 1 1 0 0 0 1 0 | r + pr + pqr + (p, q, r) |
| | | | |
| q_202 | q_11001010 | 1 1 0 0 1 0 1 0 | r + qr + pqr + (p, q, r) |
| | | | |
o---------o------------o-----------------o------------------------------o
| | | | |
| q_39 | q_00100111 | 0 0 1 0 0 1 1 1 | 1 + p + pq + pqr + (p, q, r) |
| | | | |
| q_71 | q_01000111 | 0 1 0 0 0 1 1 1 | 1 + p + pr + pqr + (p, q, r) |
| | | | |
| q_27 | q_00011011 | 0 0 0 1 1 0 1 1 | 1 + q + pq + pqr + (p, q, r) |
| | | | |
| q_83 | q_01010011 | 0 1 0 1 0 0 1 1 | 1 + q + qr + pqr + (p, q, r) |
| | | | |
| q_29 | q_00011101 | 0 0 0 1 1 1 0 1 | 1 + r + pr + pqr + (p, q, r) |
| | | | |
| q_53 | q_00110101 | 0 0 1 1 0 1 0 1 | 1 + r + qr + pqr + (p, q, r) |
| | | | |
o---------o------------o-----------------o------------------------------o
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o-------------------------------------------------o
q_216. p + p q + p q r + (p, q, r)
Jon Awbrey
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inquiry e-lab: http://stderr.org/pipermail/inquiry/
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