Geodesic
On the monochromatic Schur triples type problem
The electronic journal of combinatorics, Tome 16 (2009) no. 1
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We discuss a problem posed by Ronald Graham about the minimum number, over all 2-colorings of $[1,n]$, of monochromatic $\{x,y$, $x+ay\}$ triples for $a \geq 1$. We give a new proof of the original case of $a=1$. We show that the minimum number of such triples is at most ${n^2\over2a(a^2+2a+3)} + O(n)$ when $a \geq 2$. We also find a new upper bound for the minimum number, over all $r$-colorings of $[1,n]$, of monochromatic Schur triples, for $r \geq 3$.
DOI : 10.37236/103
Classification : 05D10
Mots-clés : minumum number, monochromatic triples 
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     author = {Thotsaporn "Aek" Thanatipanonda},
     title = {On the monochromatic {Schur} triples type problem},
     journal = {The electronic journal of combinatorics},
     year = {2009},
     volume = {16},
     number = {1},
     doi = {10.37236/103},
     zbl = {1182.05124},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/103/}
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Thotsaporn "Aek" Thanatipanonda. On the monochromatic Schur triples type problem. The electronic journal of combinatorics, Tome 16 (2009) no. 1. doi: 10.37236/103

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