2014/02/24 by Dan Saracino, Saracino, Dan
Mathematics · #05D10 #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05D10
paper · pdf · doi:10.48550/arxiv.1402.5829
7 pages
arxiv created 2014/03/10 · arxiv updated 2014/03/11
In 1982, Beutelspacher and Brestovansky determined the 2-color Rado number of the equation x1+x2+⋯ +xm-1=xm for all m≥ 3. Here we extend their result by determining the 2-color Rado number of the equation x1+x2+⋯ +xn=y1+y2+⋯ +yk for all n≥ 2 and k≥ 2. As a consequence, we determine the 2-color Rado number of x1+x2+⋯ +xn=a1y1+⋯ +aℓyℓ in all cases where n≥ 2 and n≥ a1+⋯ +aℓ, and in most cases where n≥ 2 and 2n≥ a1+⋯ +aℓ.