login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A243487 Numerator of largest minimal l^1 distance for n points in the simplex x+y+z=1, 0<=x,y,z<=1. 2

%I

%S 2,2,4,1,1,4,3,2,2,3,4,8,1,1,10,6,4,4

%N Numerator of largest minimal l^1 distance for n points in the simplex x+y+z=1, 0<=x,y,z<=1.

%C a(n) is the numerator (in lowest terms) of the maximum of min(|x_i-x_j| + |y_i-y_j| + |z_i-z_j|, 1 <= i < j <= n) where

%C x_i, y_i, z_i >= 0, x_i + y_i + z_i = 1 for 1<=i<=n.

%H Robert Israel, <a href="http://www.math.ubc.ca/~israel/packing/">A packing problem</a>

%H Robert Israel, <a href="/A243487/a243487.pdf">A packing problem</a> [Cached version, pdf format, with permission]

%H Robert Israel, <a href="https://oeis.org/A243487/a243487_3.png">Illustration for a(17), with caption</a>

%H Robert Israel, <a href="https://oeis.org/A243487/a243487_2.png">Illustration for a(17), without caption</a>

%H Math Overflow, <a href="http://mathoverflow.net/questions/168363/what-is-the-most-diverse-k-subset-of-0-1m/168476#168476">What is the most ``diverse'' k-subset of [0,1]^m?</a>

%e For n=3 an optimal configuration consists of [1,0,0],[0,1,0],[0,0,1], with all distances 2, so a(3) = 2.

%Y Denominator is A243576(n).

%K nonn,frac

%O 2,1

%A _Robert Israel_, Jun 06 2014

%E More terms from _Robert Israel_, Jun 22 2014

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified February 23 22:17 EST 2018. Contains 299595 sequences. (Running on oeis4.)