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Search: id:A064705
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| A064705 |
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Maximal number of vectors u_1, u_2, ... in R^n with |u_i| = 1 and |u_i - u_j| >= 1 for i, j distinct, where || is L1-norm. |
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+0
1
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OFFSET
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0,2
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COMMENT
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L1 norm of (a,b,c,...) = |a|+|b|+|c|+...
A lower bound if n = 2^m >= 4: a(n) >= 2n^2 + Sum_{r=2..[log_2 n]} A(2^r,2^(r-1))*A(n,2^r,2^r); compare the Edel-Rains-Sloane paper and the tables of And and Andw mentioned here - N. J. A. Sloane (njas(AT)research.att.com), Oct 12, 2001. This gives 40 in 4-D, 256 in 8-D (found also by Blokhuis), 2144 in 16-D, etc.
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LINKS
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Y. Edel, E. M. Rains and N. J. A. Sloane, New record kissing numbers in dimensions 32 to 128, Elect. J. Combin.
Y. Edel, E. M. Rains and N. J. A. Sloane, New record kissing numbers in dimensions 32 to 128
S. Litsyn, E. M. Rains and N. J. A. Sloane, A(n,d) tables.
E. M. Rains and N. J. A. Sloane, A(n,d,w) tables
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EXAMPLE
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It is easier to take the norm to be 2. For n=2: { +-2 0, 0 +-2, +-1 +-1 }; for n=3: { 200 etc. (6) and 110 etc. (12) }; for n=4: { 2000 etc. (8), 1100 etc. (24), .5 .5 .5 .5 etc. (8) }.
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CROSSREFS
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Sequence in context: A018229 A166830 A072779 this_sequence A058858 A073307 A064009
Adjacent sequences: A064702 A064703 A064704 this_sequence A064706 A064707 A064708
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KEYWORD
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nonn
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AUTHOR
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Aart Blokhuis (aartb(AT)win.tue.nl), Oct 11 2001
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