# Studies of Euler diagrams/dukeli NP/ordered

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This matrix is essentially like that shown in keyneg, but with rows and columns reordered. In this arrangement all functions in the same N-EC are in the same double column, and all functions in the same P-EC are in the same (double) row. Pairs of mirror symmetric Euler diagrams are in the same table cell. (In big cells with four diagrams they are in opposite corners.)
This is a essentially a detailed version of this table. See NP tables.
The indices of this table refer to the function dukeli. But the sequence of the columns is based on the Boolean functions' Zhegalkin indices. These numbers have a mouseover with two lines: Above the little-endian binary expression of the Zhegalkin index, and below the truth table of the Boolean function.
The rows can be ordered in four different ways:
* by binary weight of the Zhegalkin indices (5, 5, 6, 6, 6, 7, 7, 7, 8, 8)
* by number of different functions (4 rows with 12, 6 double rows with 24)
* by smallest Zhegalkin index of the row
* by number of negators in the transformation from dukeli
| W | C | | | 2290 | 2291 | 8398 | 8399 | 11278 | 11279 | 16558 | 16559 | 18958 | 18959 | 25138 | 25139 |
| 6 | 24 | 2290 | 2 | 2290 (~0, 3, ~2, 1) 3972 (~1, 2, ~3, 0) 3972 (0, ~3, 2, ~1) 2290 (1, ~2, 3, ~0) | 3970 (~0, 2, ~3, 1) 2292 (~1, 3, ~2, 0) 2292 (0, ~2, 3, ~1) 3970 (1, ~3, 2, ~0) | 8398 (~0, 3, ~1, 2) 13200 (~2, 1, ~3, 0) 13200 (0, ~3, 1, ~2) 8398 (2, ~1, 3, ~0) | 13186 (~0, 1, ~3, 2) 8412 (~2, 3, ~1, 0) 8412 (0, ~1, 3, ~2) 13186 (2, ~3, 1, ~0) | 11278 (~0, 2, ~1, 3) 14640 (~3, 1, ~2, 0) 14640 (0, ~2, 1, ~3) 11278 (3, ~1, 2, ~0) | 14386 (~0, 1, ~2, 3) 11532 (~3, 2, ~1, 0) 11532 (0, ~1, 2, ~3) 14386 (3, ~2, 1, ~0) | 16558 (~1, 3, ~0, 2) 21904 (~2, 0, ~3, 1) 21904 (1, ~3, 0, ~2) 16558 (2, ~0, 3, ~1) | 21892 (~1, 0, ~3, 2) 16570 (~2, 3, ~0, 1) 16570 (1, ~0, 3, ~2) 21892 (2, ~3, 0, ~1) | 18958 (~1, 2, ~0, 3) 22864 (~3, 0, ~2, 1) 22864 (1, ~2, 0, ~3) 18958 (3, ~0, 2, ~1) | 22612 (~1, 0, ~2, 3) 19210 (~3, 2, ~0, 1) 19210 (1, ~0, 2, ~3) 22612 (3, ~2, 0, ~1) | 25138 (~2, 1, ~0, 3) 25924 (~3, 0, ~1, 2) 25924 (2, ~1, 0, ~3) 25138 (3, ~0, 1, ~2) | 25684 (~2, 0, ~1, 3) 25378 (~3, 1, ~0, 2) 25378 (2, ~0, 1, ~3) 25684 (3, ~1, 0, ~2) |
| 7 | 24 | 2291 | 2 | 2293 (~0, ~3, 2, 1) 3971 (~1, ~2, 3, 0) 3971 (0, 3, ~2, ~1) 2293 (1, 2, ~3, ~0) | 3973 (~0, ~2, 3, 1) 2291 (~1, ~3, 2, 0) 2291 (0, 2, ~3, ~1) 3973 (1, 3, ~2, ~0) | 8413 (~0, ~3, 1, 2) 13187 (~2, ~1, 3, 0) 13187 (0, 3, ~1, ~2) 8413 (2, 1, ~3, ~0) | 13201 (~0, ~1, 3, 2) 8399 (~2, ~3, 1, 0) 8399 (0, 1, ~3, ~2) 13201 (2, 3, ~1, ~0) | 11533 (~0, ~2, 1, 3) 14387 (~3, ~1, 2, 0) 14387 (0, 2, ~1, ~3) 11533 (3, 1, ~2, ~0) | 14641 (~0, ~1, 2, 3) 11279 (~3, ~2, 1, 0) 11279 (0, 1, ~2, ~3) 14641 (3, 2, ~1, ~0) | 16571 (~1, ~3, 0, 2) 21893 (~2, ~0, 3, 1) 21893 (1, 3, ~0, ~2) 16571 (2, 0, ~3, ~1) | 21905 (~1, ~0, 3, 2) 16559 (~2, ~3, 0, 1) 16559 (1, 0, ~3, ~2) 21905 (2, 3, ~0, ~1) | 19211 (~1, ~2, 0, 3) 22613 (~3, ~0, 2, 1) 22613 (1, 2, ~0, ~3) 19211 (3, 0, ~2, ~1) | 22865 (~1, ~0, 2, 3) 18959 (~3, ~2, 0, 1) 18959 (1, 0, ~2, ~3) 22865 (3, 2, ~0, ~1) | 25379 (~2, ~1, 0, 3) 25685 (~3, ~0, 1, 2) 25685 (2, 1, ~0, ~3) 25379 (3, 0, ~1, ~2) | 25925 (~2, ~0, 1, 3) 25139 (~3, ~1, 0, 2) 25139 (2, 0, ~1, ~3) 25925 (3, 1, ~0, ~2) |
| 7 | 24 | 2298 | 3 | 2298 (~0, ~3, ~2, 1) 3980 (~1, ~2, ~3, 0) 3980 (0, ~3, ~2, ~1) 2298 (1, ~2, ~3, ~0) | 3978 (~0, ~2, ~3, 1) 2300 (~1, ~3, ~2, 0) 2300 (0, ~2, ~3, ~1) 3978 (1, ~3, ~2, ~0) | 8430 (~0, ~3, ~1, 2) 13232 (~2, ~1, ~3, 0) 13232 (0, ~3, ~1, ~2) 8430 (2, ~1, ~3, ~0) | 13218 (~0, ~1, ~3, 2) 8444 (~2, ~3, ~1, 0) 8444 (0, ~1, ~3, ~2) 13218 (2, ~3, ~1, ~0) | 11790 (~0, ~2, ~1, 3) 15152 (~3, ~1, ~2, 0) 15152 (0, ~2, ~1, ~3) 11790 (3, ~1, ~2, ~0) | 14898 (~0, ~1, ~2, 3) 12044 (~3, ~2, ~1, 0) 12044 (0, ~1, ~2, ~3) 14898 (3, ~2, ~1, ~0) | 16622 (~1, ~3, ~0, 2) 21968 (~2, ~0, ~3, 1) 21968 (1, ~3, ~0, ~2) 16622 (2, ~0, ~3, ~1) | 21956 (~1, ~0, ~3, 2) 16634 (~2, ~3, ~0, 1) 16634 (1, ~0, ~3, ~2) 21956 (2, ~3, ~0, ~1) | 19982 (~1, ~2, ~0, 3) 23888 (~3, ~0, ~2, 1) 23888 (1, ~2, ~0, ~3) 19982 (3, ~0, ~2, ~1) | 23636 (~1, ~0, ~2, 3) 20234 (~3, ~2, ~0, 1) 20234 (1, ~0, ~2, ~3) 23636 (3, ~2, ~0, ~1) | 29234 (~2, ~1, ~0, 3) 30020 (~3, ~0, ~1, 2) 30020 (2, ~1, ~0, ~3) 29234 (3, ~0, ~1, ~2) | 29780 (~2, ~0, ~1, 3) 29474 (~3, ~1, ~0, 2) 29474 (2, ~0, ~1, ~3) 29780 (3, ~1, ~0, ~2) |
| 8 | 24 | 2299 | 1 | 2301 (~0, 3, 2, 1) 3979 (~1, 2, 3, 0) 3979 (0, 3, 2, ~1) 2301 (1, 2, 3, ~0) | 3981 (~0, 2, 3, 1) 2299 (~1, 3, 2, 0) 2299 (0, 2, 3, ~1) 3981 (1, 3, 2, ~0) | 8445 (~0, 3, 1, 2) 13219 (~2, 1, 3, 0) 13219 (0, 3, 1, ~2) 8445 (2, 1, 3, ~0) | 13233 (~0, 1, 3, 2) 8431 (~2, 3, 1, 0) 8431 (0, 1, 3, ~2) 13233 (2, 3, 1, ~0) | 12045 (~0, 2, 1, 3) 14899 (~3, 1, 2, 0) 14899 (0, 2, 1, ~3) 12045 (3, 1, 2, ~0) | 15153 (~0, 1, 2, 3) 11791 (~3, 2, 1, 0) 11791 (0, 1, 2, ~3) 15153 (3, 2, 1, ~0) | 16635 (~1, 3, 0, 2) 21957 (~2, 0, 3, 1) 21957 (1, 3, 0, ~2) 16635 (2, 0, 3, ~1) | 21969 (~1, 0, 3, 2) 16623 (~2, 3, 0, 1) 16623 (1, 0, 3, ~2) 21969 (2, 3, 0, ~1) | 20235 (~1, 2, 0, 3) 23637 (~3, 0, 2, 1) 23637 (1, 2, 0, ~3) 20235 (3, 0, 2, ~1) | 23889 (~1, 0, 2, 3) 19983 (~3, 2, 0, 1) 19983 (1, 0, 2, ~3) 23889 (3, 2, 0, ~1) | 29475 (~2, 1, 0, 3) 29781 (~3, 0, 1, 2) 29781 (2, 1, 0, ~3) 29475 (3, 0, 1, ~2) | 30021 (~2, 0, 1, 3) 29235 (~3, 1, 0, 2) 29235 (2, 0, 1, ~3) 30021 (3, 1, 0, ~2) |
| 5 | 24 | 2754 | 3 | 2756 (~0, ~3, 2, ~1) 2754 (~1, ~2, 3, ~0) 2754 (~0, 3, ~2, ~1) 2756 (~1, 2, ~3, ~0) | 3236 (~0, ~2, 3, ~1) 3234 (~1, ~3, 2, ~0) 3234 (~0, 2, ~3, ~1) 3236 (~1, 3, ~2, ~0) | 8912 (~0, ~3, 1, ~2) 8898 (~2, ~1, 3, ~0) 8898 (~0, 3, ~1, ~2) 8912 (~2, 1, ~3, ~0) | 12440 (~0, ~1, 3, ~2) 12426 (~2, ~3, 1, ~0) 12426 (~0, 1, ~3, ~2) 12440 (~2, 3, ~1, ~0) | 11552 (~0, ~2, 1, ~3) 11298 (~3, ~1, 2, ~0) 11298 (~0, 2, ~1, ~3) 11552 (~3, 1, ~2, ~0) | 14600 (~0, ~1, 2, ~3) 14346 (~3, ~2, 1, ~0) 14346 (~0, 1, ~2, ~3) 14600 (~3, 2, ~1, ~0) | 17584 (~1, ~3, 0, ~2) 17572 (~2, ~0, 3, ~1) 17572 (~1, 3, ~0, ~2) 17584 (~2, 0, ~3, ~1) | 20632 (~1, ~0, 3, ~2) 20620 (~2, ~3, 0, ~1) 20620 (~1, 0, ~3, ~2) 20632 (~2, 3, ~0, ~1) | 19264 (~1, ~2, 0, ~3) 19012 (~3, ~0, 2, ~1) 19012 (~1, 2, ~0, ~3) 19264 (~3, 0, ~2, ~1) | 22792 (~1, ~0, 2, ~3) 22540 (~3, ~2, 0, ~1) 22540 (~1, 0, ~2, ~3) 22792 (~3, 2, ~0, ~1) | 25408 (~2, ~1, 0, ~3) 25168 (~3, ~0, 1, ~2) 25168 (~2, 1, ~0, ~3) 25408 (~3, 0, ~1, ~2) | 25888 (~2, ~0, 1, ~3) 25648 (~3, ~1, 0, ~2) 25648 (~2, 0, ~1, ~3) 25888 (~3, 1, ~0, ~2) |
| 6 | 24 | 2755 | 1 | 3237 (0, ~3, 2, 1) 3235 (1, ~2, 3, 0) 3235 (0, 3, ~2, 1) 3237 (1, 2, ~3, 0) | 2757 (0, ~2, 3, 1) 2755 (1, ~3, 2, 0) 2755 (0, 2, ~3, 1) 2757 (1, 3, ~2, 0) | 12441 (0, ~3, 1, 2) 12427 (2, ~1, 3, 0) 12427 (0, 3, ~1, 2) 12441 (2, 1, ~3, 0) | 8913 (0, ~1, 3, 2) 8899 (2, ~3, 1, 0) 8899 (0, 1, ~3, 2) 8913 (2, 3, ~1, 0) | 14601 (0, ~2, 1, 3) 14347 (3, ~1, 2, 0) 14347 (0, 2, ~1, 3) 14601 (3, 1, ~2, 0) | 11553 (0, ~1, 2, 3) 11299 (3, ~2, 1, 0) 11299 (0, 1, ~2, 3) 11553 (3, 2, ~1, 0) | 20633 (1, ~3, 0, 2) 20621 (2, ~0, 3, 1) 20621 (1, 3, ~0, 2) 20633 (2, 0, ~3, 1) | 17585 (1, ~0, 3, 2) 17573 (2, ~3, 0, 1) 17573 (1, 0, ~3, 2) 17585 (2, 3, ~0, 1) | 22793 (1, ~2, 0, 3) 22541 (3, ~0, 2, 1) 22541 (1, 2, ~0, 3) 22793 (3, 0, ~2, 1) | 19265 (1, ~0, 2, 3) 19013 (3, ~2, 0, 1) 19013 (1, 0, ~2, 3) 19265 (3, 2, ~0, 1) | 25889 (2, ~1, 0, 3) 25649 (3, ~0, 1, 2) 25649 (2, 1, ~0, 3) 25889 (3, 0, ~1, 2) | 25409 (2, ~0, 1, 3) 25169 (3, ~1, 0, 2) 25169 (2, 0, ~1, 3) 25409 (3, 1, ~0, 2) |
| 5 | 12 | 2760 | 4 | 2760 (~0, ~3, ~2, ~1) 2760 (~1, ~2, ~3, ~0) | 3240 (~0, ~2, ~3, ~1) 3240 (~1, ~3, ~2, ~0) | 8928 (~0, ~3, ~1, ~2) 8928 (~2, ~1, ~3, ~0) | 12456 (~0, ~1, ~3, ~2) 12456 (~2, ~3, ~1, ~0) | 11808 (~0, ~2, ~1, ~3) 11808 (~3, ~1, ~2, ~0) | 14856 (~0, ~1, ~2, ~3) 14856 (~3, ~2, ~1, ~0) | 17632 (~1, ~3, ~0, ~2) 17632 (~2, ~0, ~3, ~1) | 20680 (~1, ~0, ~3, ~2) 20680 (~2, ~3, ~0, ~1) | 20032 (~1, ~2, ~0, ~3) 20032 (~3, ~0, ~2, ~1) | 23560 (~1, ~0, ~2, ~3) 23560 (~3, ~2, ~0, ~1) | 29248 (~2, ~1, ~0, ~3) 29248 (~3, ~0, ~1, ~2) | 29728 (~2, ~0, ~1, ~3) 29728 (~3, ~1, ~0, ~2) |
| 6 | 12 | 2761 | 0 | 3241 (0, 3, 2, 1) 3241 (1, 2, 3, 0) | 2761 (0, 2, 3, 1) 2761 (1, 3, 2, 0) | 12457 (0, 3, 1, 2) 12457 (2, 1, 3, 0) | 8929 (0, 1, 3, 2) 8929 (2, 3, 1, 0) | 14857 (0, 2, 1, 3) 14857 (3, 1, 2, 0) | 11809 (0, 1, 2, 3) 11809 (3, 2, 1, 0) | 20681 (1, 3, 0, 2) 20681 (2, 0, 3, 1) | 17633 (1, 0, 3, 2) 17633 (2, 3, 0, 1) | 23561 (1, 2, 0, 3) 23561 (3, 0, 2, 1) | 20033 (1, 0, 2, 3) 20033 (3, 2, 0, 1) | 29729 (2, 1, 0, 3) 29729 (3, 0, 1, 2) | 29249 (2, 0, 1, 3) 29249 (3, 1, 0, 2) |
| 7 | 12 | 2766 | 2 | 2766 (~0, 3, 2, ~1) 2766 (~1, 2, 3, ~0) | 3246 (~0, 2, 3, ~1) 3246 (~1, 3, 2, ~0) | 8946 (~0, 3, 1, ~2) 8946 (~2, 1, 3, ~0) | 12474 (~0, 1, 3, ~2) 12474 (~2, 3, 1, ~0) | 12066 (~0, 2, 1, ~3) 12066 (~3, 1, 2, ~0) | 15114 (~0, 1, 2, ~3) 15114 (~3, 2, 1, ~0) | 17652 (~1, 3, 0, ~2) 17652 (~2, 0, 3, ~1) | 20700 (~1, 0, 3, ~2) 20700 (~2, 3, 0, ~1) | 20292 (~1, 2, 0, ~3) 20292 (~3, 0, 2, ~1) | 23820 (~1, 0, 2, ~3) 23820 (~3, 2, 0, ~1) | 29520 (~2, 1, 0, ~3) 29520 (~3, 0, 1, ~2) | 30000 (~2, 0, 1, ~3) 30000 (~3, 1, 0, ~2) |
| 8 | 12 | 2767 | 2 | 3247 (0, ~3, ~2, 1) 3247 (1, ~2, ~3, 0) | 2767 (0, ~2, ~3, 1) 2767 (1, ~3, ~2, 0) | 12475 (0, ~3, ~1, 2) 12475 (2, ~1, ~3, 0) | 8947 (0, ~1, ~3, 2) 8947 (2, ~3, ~1, 0) | 15115 (0, ~2, ~1, 3) 15115 (3, ~1, ~2, 0) | 12067 (0, ~1, ~2, 3) 12067 (3, ~2, ~1, 0) | 20701 (1, ~3, ~0, 2) 20701 (2, ~0, ~3, 1) | 17653 (1, ~0, ~3, 2) 17653 (2, ~3, ~0, 1) | 23821 (1, ~2, ~0, 3) 23821 (3, ~0, ~2, 1) | 20293 (1, ~0, ~2, 3) 20293 (3, ~2, ~0, 1) | 30001 (2, ~1, ~0, 3) 30001 (3, ~0, ~1, 2) | 29521 (2, ~0, ~1, 3) 29521 (3, ~1, ~0, 2) |