The Hypercube nPan4k | |||
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nPan4k = OddSwap(nN4k _[0,..,2k-1,4k-1,..,2k]) | |||
{pan-(2l+1 ; l=0..n\2)-agonal pan-n-agonal compact complete} | |||
nPan4k([xi]) = nN4k({perm[(x + ((Odd([xi]) ? 2k : 0)) % 4k]}i) = i=0∑n-1 {perm[(x + ((Odd([xi]) ? 2k : 0)) % 4k]}i (4k)i with perm = [0,..,2k-1,4k-1,..,2k] |
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"even" position "odd" position |
an n-Point with values summing either too an odd or even number | ||
Even([xi]) are: [xi] with: (i=0∑n-1 xi) % 2 = 0 Odd([xi]) are: [xi] with: (i=0∑n-1 xi) % 2 = 1 |
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"even" vector "odd" vector |
an n-Vector with values summing either too an odd or even number | ||
Even(<xi>) are: <xi> with: (i=0∑n-1 xi) % 2 = 0 Odd(<xi>) are: <xi> with: (i=0∑n-1 xi) % 2 = 1 |
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OddSwap(n-Point) | half n-agonal swapping of odd n-Points | ||
OddSwap([xi]) = [xi] when Even([xi]) OddSwap([xi]) = [((x + 2k) % 4k)i] when Odd([xi]) |
The Panmagic squares order 4 starting with 2Pan4^[1,0] (=square #178) | ||||||||
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group of (group-)order 48 combining two groups: GS-group of order 6 generated by {N4} {2N1 2N4} and {N2 N2} (tables vertical) group of order 8 generated by @[2,1]_1[0,3,2,1] and _3[0,3,2,1] (tables horizontal) |
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square #178 | @[2,1]_1[0,3,2,1] | (@[2,1]_1[0,3,2,1])2 | (@[2,1]_1[0,3,2,1])3 | _3[0,3,2,1] | _3[0,3,2,1] | _3[0,3,2,1] | _3[0,3,2,1] | @[2,1]_1[0,3,2,1] | @[2,1]_2[0,3,2,1] | @[0,2] | @[0,2]_3[0,3,2,1] | @[2,3]_1[0,3,2,1] | @[2,3]_2[0,3,2,1] |
{N4} |
01 12 13 08 15 06 03 10 04 09 16 05 14 07 02 11 |
01 08 13 12 14 11 02 07 04 05 16 09 15 10 03 06 |
03 06 15 10 16 09 04 05 02 07 14 11 13 12 01 08 |
03 10 15 06 13 08 01 12 02 11 14 07 16 05 04 09 |
04 09 16 05 14 07 02 11 01 12 13 08 15 06 03 10 |
04 05 16 09 15 10 03 06 01 08 13 12 14 11 02 07 |
02 07 14 11 13 12 01 08 03 06 15 10 16 09 04 05 |
02 11 14 07 16 05 04 09 03 10 15 06 13 08 01 12 |
{2N1 2N4} |
01 14 07 12 15 04 09 06 10 05 16 03 08 11 02 13 |
01 12 07 14 08 13 02 11 10 03 16 05 15 06 09 04 |
09 04 15 06 16 05 10 03 02 11 08 13 07 14 01 12 |
09 06 15 04 07 12 01 14 02 13 08 11 16 03 10 05 |
10 05 16 03 08 11 02 13 01 14 07 12 15 04 09 06 |
10 03 16 05 15 06 09 04 01 12 07 14 08 13 02 11 |
02 11 08 13 07 14 01 12 09 04 15 06 16 05 10 03 |
02 13 08 11 16 03 10 05 09 06 15 04 07 12 01 14 |
{N2 N2} |
01 14 11 08 15 04 05 10 06 09 16 03 12 07 02 13 |
01 08 11 14 12 13 02 07 06 03 16 09 15 10 05 04 |
05 04 15 10 16 09 06 03 02 07 12 13 11 14 01 08 |
05 10 15 04 11 08 01 14 02 13 12 07 16 03 06 09 |
06 09 16 03 12 07 02 13 01 14 11 08 15 04 05 10 |
06 03 16 09 15 10 05 04 01 08 11 14 12 13 02 07 |
02 07 12 13 11 14 01 08 05 04 15 10 16 09 06 03 |
02 13 12 07 16 03 06 09 05 10 15 04 11 08 01 14 |
{{2N1 2N4} (2N1 2N4)} |
01 08 11 14 15 10 05 04 06 03 16 09 12 13 02 07 |
01 14 11 08 12 07 02 13 06 09 16 03 15 04 05 10 |
05 10 15 04 16 03 06 09 02 13 12 07 11 08 01 14 |
05 04 15 10 11 14 01 08 02 07 12 13 16 09 06 03 |
06 03 16 09 12 13 02 07 01 08 11 14 15 10 05 04 |
06 09 16 03 15 04 05 10 01 14 11 08 12 07 02 13 |
02 13 12 07 11 08 01 14 05 10 15 04 16 03 06 09 |
02 07 12 13 16 09 06 03 05 04 15 10 11 14 01 08 |
{{N2 N2} (2N1 2N4)} |
01 12 07 14 15 06 09 04 10 03 16 05 08 13 02 11 |
01 14 07 12 08 11 02 13 10 05 16 03 15 04 09 06 |
09 06 15 04 16 03 10 05 02 13 08 11 07 12 01 14 |
09 04 15 06 07 14 01 12 02 11 08 13 16 05 10 03 |
10 03 16 05 08 13 02 11 01 12 07 14 15 06 09 04 |
10 05 16 03 15 04 09 06 01 14 07 12 08 11 02 13 |
02 13 08 11 07 12 01 14 09 06 15 04 16 03 10 05 |
02 11 08 13 16 05 10 03 09 04 15 06 07 14 01 12 |
{{2N1 2N4} (N2 N2)} |
01 08 13 12 15 10 03 06 04 05 16 09 14 11 02 07 |
01 12 13 08 14 07 02 11 04 09 16 05 15 06 03 10 |
03 10 15 06 16 05 04 09 02 11 14 07 13 08 01 12 |
03 06 15 10 13 12 01 08 02 07 14 11 16 09 04 05 |
04 05 16 09 14 11 02 07 01 08 13 12 15 10 03 06 |
04 09 16 05 15 06 03 10 01 12 13 08 14 07 02 11 |
02 11 14 07 13 08 01 12 03 10 15 06 16 05 04 09 |
02 07 14 11 16 09 04 05 03 06 15 10 13 12 01 08 |