On the Minimum Number of Monochromatic Generalized Schur Triples

Abstract

The solution to the problem of finding the minimum number of monochromatic triples (x, y, x + ay) with a > 2 being a fixed positive integer over any 2-coloring of [1, n] was conjectured by Butler, Costello, and Graham (2010) and Thanathipanonda (2009). We solve this problem using a method based on Datskovsky’s proof (2003) on the minimum number of monochromatic Schur triples (x, y, x + y). We do this by exploiting the combinatorial nature of the original proof and adapting it to the general problem.

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Cite this paper

@article{Thanatipanonda2017OnTM, title={On the Minimum Number of Monochromatic Generalized Schur Triples}, author={Thotsaporn Thanatipanonda and Elaine Wong}, journal={Electr. J. Comb.}, year={2017}, volume={24}, pages={P2.20} }