Category:4-ary Zhegalkin indices in 16-cube matrix; great principalities; with entries in top row
3-ary (4) | 4-ary (20) | great principalities with entries | on diagonal (related to patron dominions) |
3-ary (4) | 4-ary (22) | in top row (related to patron principalities) |
The following 22 (of 272) great principalities contain Boolean functions whose Zhegalkin indices are 0 in the less significant half of bits:
[0, 2, 8, 10, 40, 42, 128, 138, 168, 552, 554, 642, 648, 682, 2178, 2184, 2208, 2722, 10368, 10378, 10408, 10922]
They are in the top row of the 256×256 matrix. Their positions on it are shown in a 16×16 matrix.
The 16×16 matrices show a relationship to the Zhegalkin indices of 3-ary principalities. Each one is indicated by the small king index.
The entries in a 16×16 matrix are either evil or odious. (See the odious pattern.)
They form pairs that differ only in the most significant bit.
The combined entries of these two matrices form the transpose of the 16×16 matrix shown on the left.
nobles | |
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partial relationship with super-clans | |
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Surprisingly, there is some similarity between the patterns of top-row entries and 3-ary super clans. | |
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Subcategories
This category has the following 2 subcategories, out of 2 total.
Media in category "4-ary Zhegalkin indices in 16-cube matrix; great principalities; with entries in top row"
The following 22 files are in this category, out of 22 total.
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4Z principality; faction size 10; king index 128.svg 1,560 × 1,560; 1 KB
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4Z principality; faction size 10; king index 2184.svg 1,560 × 1,560; 1 KB
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4Z principality; faction size 15; king index 10.svg 1,560 × 1,560; 1 KB
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4Z principality; faction size 15; king index 10378.svg 1,560 × 1,560; 1 KB
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4Z principality; faction size 15; king index 10408.svg 1,560 × 1,560; 1 KB
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4Z principality; faction size 15; king index 40.svg 1,560 × 1,560; 1 KB
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4Z principality; faction size 1; king index 0.svg 1,560 × 1,560; 653 bytes
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4Z principality; faction size 20; king index 2.svg 1,560 × 1,560; 2 KB
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4Z principality; faction size 20; king index 2722.svg 1,560 × 1,560; 2 KB
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4Z principality; faction size 20; king index 552.svg 1,560 × 1,560; 2 KB
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4Z principality; faction size 30; king index 168.svg 1,560 × 1,560; 2 KB
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4Z principality; faction size 30; king index 642.svg 1,560 × 1,560; 2 KB
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4Z principality; faction size 30; king index 682.svg 1,560 × 1,560; 2 KB
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4Z principality; faction size 30; king index 8.svg 1,560 × 1,560; 2 KB
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4Z principality; faction size 5; king index 10368.svg 1,560 × 1,560; 849 bytes
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4Z principality; faction size 5; king index 10922.svg 1,560 × 1,560; 857 bytes
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4Z principality; faction size 5; king index 554.svg 1,560 × 1,560; 885 bytes
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4Z principality; faction size 60; king index 138.svg 1,560 × 1,560; 4 KB
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4Z principality; faction size 60; king index 2178.svg 1,560 × 1,560; 4 KB
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4Z principality; faction size 60; king index 2208.svg 1,560 × 1,560; 3 KB
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4Z principality; faction size 60; king index 42.svg 1,560 × 1,560; 4 KB
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4Z principality; faction size 60; king index 648.svg 1,560 × 1,560; 4 KB