논문KCI 등재
2-COLOR RADO NUMBER FOR x1 + x2 + · · · + xn = y1 + y2 = z
1
조회
0
다운로드
0
인용
0
참고문헌
키워드
주제분류수학
초록
An r-color Rado number N = R(L, r) for a system L of equations is the least integer, provided it exists, such that for every r-coloring of the set {1, 2, . . . , N}, there is a monochromatic solution to L. In this paper, we study the 2-color Rado number R(E, 2) for E : x1 + x2 + · · · + xn = y1 + y2 = z when n ≥ 4.
Abstract
An r-color Rado number N = R(L, r) for a system L of equations is the least integer, provided it exists, such that for every r-coloring of the set {1, 2, . . . , N}, there is a monochromatic solution to L. In this paper, we study the 2-color Rado number R(E, 2) for E : x1 + x2 + · · · + xn = y1 + y2 = z when n ≥ 4.
참고문헌 (18)
- T. Ahmed, "On generalized Schur numbers", Exp. Math, 25, pp.213~218 (2016)
- A. Beutelspacher, "Generalized Schur number", Lecture Notes in Math, 969, pp.30~38 (1982)
- W. Deuber, "Survey Combin", pp.52~74 (1989), Cambridge University Press
- S. Guo, "Determination of the two-color Rado number for a1x1 +· · · + amxm = x0", J. Combin. Theory Ser. A, 115, pp.345~353 (2008)
- M.J.H. Heule, "Schur number five", The Thirty-Second AAAI Conference on Arti ficial Intelligence (AAAI-18) (2018)
- H. Harborth, "Rado numbers for a(x + y) = bz", J. Combin. Theory Ser. A, 80, pp.356~363 (1997)
- H. Harborth, "All two-color Rado numbers for a(x + y) = bz", Discrete Math, 197, pp.198 (1999), 397~407
- B. Hopkins, "On Rado numbers for ∑m-1i=1 aixi = xm", Adv. in Appl. Math, 35, pp.433~441 (2005)
- W. Kosek, "A note on disjunctive Rado numbers", Adv. in Appl. Math, 31, pp.433~439 (2003)
- R. Rado, "Studien zur Kombinatorik", Math. Z, 36, pp.424~480 (1933)
- A. Robertson, "Some two color, four variable Rado numbers", Adv. in Appl. Math, 41, pp.214~226 (2008)
- A. Robertson, "Off-diagonal generalized Schur numbers", Adv. in Appl. Math, 26, pp.252~257 (2001)
- D. Saracino, "The 2-color rado number of x1 +x2 +· · ·+xn = y1 +y2 +· · ·+yk", Ars Combinatoria, 129, pp.315~321 (2016)
- D. Saracino, "The 2-color rado number of x1 + x2 + · · · + xm-1 = axm", Ars Combinatoria, 113, pp.81~95 (2014)
- D. Saracino, "The 2-color rado number of x1 + x2 + · · · + xm-1 = axm, II", Ars Combinatoria, 119, pp.193~210 (2015)
- D. Saracino, "The 2-color Rado number of x + y + kz = 3w", Ars Combinatoria, 90, pp.119~127 (2009)
- I. Schur, "Über die Kongruenz xm + ym ≡ zm(mod p)", Jahresber. Deutsch. Math. -Verein, 25, pp.114~117 (1916)
- W. Wallis, "Combinatorics: Room Squares, Sum-Free Sets, Hadamard Matrices", Lecture Notes in Math, 48 (1972), Springer
관련 논문AI추천
A note on the mixed van der Waerden numberKai An Sim, Kok Bin Wong, Ta Sheng Tan대한수학회 · 대한수학회보2021 · 제58권 제6호AN ANALOGUE OF THE HILTON-MILNER THEOREM FOR WEAK COMPOSITIONSCheng Yeaw Ku, Kok Bin Wong대한수학회 · 대한수학회보2015 · 제52권 제3호A note on Snevily's conjecture in set systems김연진, 황경원, Rudy X. J. Liu장전수학회 · Advanced Studies in Contemporary Mathematics2017 · 제27권 제1호An analogue of the Erd{\H o}s matching conjecture for weak compositionsCheng Yeaw Ku, Kok Bin Wong대한수학회 · 대한수학회보2025 · 제62권 제5호Characterization of finite colored spaces with certain conditionsMasashi Shinohara, Mitsugu Hirasaka대한수학회 · 대한수학회지2019 · 제56권 제3호An Erdos-Ko-Rado theorem for minimal coversCheng Yeaw Ku, Kok Bin Wong대한수학회 · 대한수학회보2017 · 제54권 제3호
이 간행물의 다른 논문 (15건)
Hyers-Ulam-Rassias stability of a quadratic-cubic-quartic functional equation이양희pp. 159-168A Common fixed point theorem on ordered partial S-metric spaces and applicationsSima Soursouri, Ishak Altun, Nabi Shobkolaei, Sahaban Sedghipp. 169-189Powers of integers with arithmetic tables최은미, 최명진pp. 191-203A new paranormed series space using Euler totient means and some matrix transformationsG. Canan Hazar Gulec, Merve Ilkhanpp. 205-221Almost periodic solutions of periodic second order linear evolution equationsVu Trong Luong, Nguyen Van Minh, Bui Xuan Dieu, Nguyen Huu Tripp. 223-240