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@hacklex
Created February 9, 2024 12:39
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Heisenberg group over Z2, zero-point distances histograms
Order = 1
# 0 1 2
hist 1 3 4
Δ 1 1 -2
2C₂ᵏ 2 4 2
NoZ Δ 1 2 0
NoZHist 1 2 2 2 1
Order = 2
# 0 1 2 3 4
hist 1 5 12 12 2
Δ 1 3 0 -4 0
2C₄ᵏ 2 8 12 8 2
NoZ Δ 1 4 4 -4 -5
NoZHist 1 4 8 12 7
Order = 3
# 0 1 2 3 4 5 6
hist 1 7 24 44 38 12 2
Δ 1 5 6 -4 -8 0 0
2C₆ᵏ 2 12 30 40 30 12 2
NoZ Δ 1 6 12 2 -13 -8 0
NoZHist 1 6 18 38 43 20 2
Order = 4
# 0 1 2 3 4 5 6 7 8
hist 1 9 40 104 156 128 56 16 2
Δ 1 7 16 8 -16 -16 0 0 0
2C₈ᵏ 2 16 56 112 140 112 56 16 2
NoZ Δ 1 8 24 24 -9 -32 -16 0 0
NoZHist 1 8 32 88 149 144 72 16 2
Order = 5
# 0 1 2 3 4 5 6 7 8 9 10
hist 1 11 60 200 420 552 452 240 90 20 2
Δ 1 9 30 40 0 -48 -32 0 0 0 0
2C₁₀ᵏ 2 20 90 240 420 504 420 240 90 20 2
NoZ Δ 1 10 40 70 39 -48 -80 -32 0 0 0
NoZHist 1 10 50 170 381 552 500 272 90 20 2
Order = 6
# 0 1 2 3 4 5 6 7 8 9 10 11 12
hist 1 13 84 340 910 1632 1976 1648 990 440 132 24 2
Δ 1 11 48 100 80 -48 -128 -64 0 0 0 0 0
2C₁₂ᵏ 2 24 132 440 990 1584 1848 1584 990 440 132 24 2
NoZ Δ 1 12 60 148 179 32 -176 -192 -64 0 0 0 0
NoZHist 1 12 72 292 811 1552 2024 1776 1054 440 132 24 2
Order = 7
# 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
hist 1 15 112 532 1722 3892 6230 7184 6134 4004 2002 728 182 28 2
Δ 1 13 70 196 280 112 -224 -320 -128 0 0 0 0 0 0
2C₁₄ᵏ 2 28 182 728 2002 4004 6006 6864 6006 4004 2002 728 182 28 2
NoZ Δ 1 14 84 266 475 392 -112 -544 -448 -128 0 0 0 0 0
NoZHist 1 14 98 462 1527 3612 6118 7408 6454 4132 2002 728 182 28 2
Order = 8
# 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
hist 1 17 144 784 2968 8064 16016 23648 26508 23136 16016 8736 3640 1120 240 32 2
Δ 1 15 96 336 672 672 0 -768 -768 -256 0 0 0 0 0 0 0
2C₁₆ᵏ 2 32 240 1120 3640 8736 16016 22880 25740 22880 16016 8736 3640 1120 240 32 2
NoZ Δ 1 16 112 432 1007 1344 672 -768 -1536 -1024 -256 0 0 0 0 0 0
NoZHist 1 16 128 688 2633 7392 15344 23648 27276 23904 16272 8736 3640 1120 240 32 2
Order = 9
# 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
hist 1 19 180 1104 4776 15120 35784 64416 89820 99032 88028 63648 37128 17136 6120 1632 306 36 2
Δ 1 17 126 528 1344 2016 1344 -768 -2304 -1792 -512 0 0 0 0 0 0 0 0
2C₁₈ᵏ 2 36 306 1632 6120 17136 37128 63648 87516 97240 87516 63648 37128 17136 6120 1632 306 36 2
NoZ Δ 1 18 144 654 1871 3360 3360 576 -3072 -4096 -2304 -512 0 0 0 0 0 0 0
NoZHist 1 18 162 978 4249 13776 33768 63072 90588 101336 89820 64160 37128 17136 6120 1632 306 36 2
Order = 10
# 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
hist 1 21 220 1500 7290 26304 72144 153120 255780 342320 373608 336944 251940 155040 77520 31008 9690 2280 380 40 2
Δ 1 19 160 780 2400 4704 5376 1920 -3840 -6400 -4096 -1024 0 0 0 0 0 0 0 0 0
2C₂₀ᵏ 2 40 380 2280 9690 31008 77520 155040 251940 335920 369512 335920 251940 155040 77520 31008 9690 2280 380 40 2
NoZ Δ 1 20 180 940 3179 7104 10080 7296 -1920 -10240 -10496 -5120 -1024 0 0 0 0 0 0 0 0
NoZHist 1 20 200 1340 6511 23904 67440 147744 253860 346160 380008 341040 252964 155040 77520 31008 9690 2280 380 40 2
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