On Some Numbers Related to the Erdös-Szekeres TheoremReport as inadecuate




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A crossing family ofsegments is a collection of segments each pair of which crosses. Given positiveintegers j and k,aj,k grid is the union of two pairwise-disjointcollections of segments with j and k members, respectively such that each segmentin the first collection crosses all members of the other. Let ck be the least integer such that any planar setof ck points in general position generates acrossing family of k segments. Also let #j,k be the least integer such that any planar setof #j,k points in general position generates a j,k-grid. We establish here thefacts 9≤c3≤16 and #1,2=8.

KEYWORDS

Erdos-Szekeres Theorem; Combinatorial Geometry

Cite this paper

M. Nielsen and W. Webb -On Some Numbers Related to the Erdös-Szekeres Theorem,- Open Journal of Discrete Mathematics, Vol. 3 No. 3, 2013, pp. 167-173. doi: 10.4236-ojdm.2013.33030.





Author: Mark J. Nielsen, William Webb

Source: http://www.scirp.org/



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