[seqfan] Minimum number of points on an n X k grid forcing the formation of isoceles triangles

Bob Selcoe rselcoe at entouchonline.net
Mon Apr 25 21:36:31 CEST 2016


Hi Seqfans,

A271914 shows the array for maximum number of points that can be chosen in
an n X k grid such that no three distinct points form an isosceles triangle.

But what about the minimum number T(n,k) that can be chosen so that no three 
distinct points form an isosceles triangle, but any
additional point will form of one?  We can safely say T(n,1) = n; but beyond 
that it gets more interesting
and might make a nice companion entry tor A271914.

So for example, T(9,1) = 9, but T(9,3) <= 7:

o o X o o X X X X
o o X o o o o o o
o o X o o o o o o

There are many other configurations with 7 points.  Any < 7?

Cheers,
Bob Selcoe





 



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