Large convex sets in difference sets
Copyright policy )Large convex sets in difference sets
AbstractWe give a construction of a convex set with cardinality such that contains a convex subset with cardinality . We also consider the following variant of this problem: given a convex set , what is the size of the largest matching such that the set is convex? We prove that there always exists such an with , and that this lower bound is best possible, up to a multiplicative constant.
- Austrian Academy of Sciences Austria
- Johann Radon Institute for Computational and Applied Mathematics Austria
- Johannes Kepler University of Linz Austria
- Institute for Basic Science Korea (Republic of)
Arithmetic combinatorics; higher degree uniformity, convex sets, Other combinatorial number theory, FOS: Mathematics, sumsets, Mathematics - Combinatorics, Other problems of combinatorial convexity, Combinatorics (math.CO), difference sets
Arithmetic combinatorics; higher degree uniformity, convex sets, Other combinatorial number theory, FOS: Mathematics, sumsets, Mathematics - Combinatorics, Other problems of combinatorial convexity, Combinatorics (math.CO), difference sets
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