TY - JOUR
T1 - On the minimum number of monochromatic generalized Schur triples
AU - Thanatipanonda, Thotsaporn
AU - Wong, Elaine
N1 - Publisher Copyright:
© 2017, Australian National University. All rights reserved.
PY - 2017/5/5
Y1 - 2017/5/5
N2 - 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.
AB - 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.
KW - Optimization
KW - Rado Equation
KW - Ramsey Theory on Integers
KW - Schur Triples
UR - http://www.scopus.com/inward/record.url?scp=85019119627&partnerID=8YFLogxK
U2 - 10.37236/6490
DO - 10.37236/6490
M3 - Article
AN - SCOPUS:85019119627
SN - 1077-8926
VL - 24
JO - Electronic Journal of Combinatorics
JF - Electronic Journal of Combinatorics
IS - 2
M1 - #P2.20
ER -