Rado numbers of regular nonhomogeneous equations

Thotsaporn Thanatipanonda

Rado numbers of regular nonhomogeneous equations

Thotsaporn Thanatipanonda

Science Division

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

We consider Rado numbers of the regular equations E_k (b) of the form c₁x₁ + c₂x₂ + · · · + c_k−1 x_k−1 = x_k + b, where b ∈ Z and c_i ∈ Z⁺ for all i. We give universal upper bounds and qualified lower bounds for t-color Rado numbers r(E_k (b); t) in terms of r(E_k (0); t). The qualification is based on a new concept we name the excellence condition. We also give examples where the exact values of Rado numbers are obtained from these results.

Original language	English
Pages (from-to)	5-10
Number of pages	6
Journal	Discrete Mathematics Letters
Volume	4
Publication status	Published - 2020

Keywords

Experimental mathematics
Ramsey theory

Cite this

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title = "Rado numbers of regular nonhomogeneous equations",

abstract = "We consider Rado numbers of the regular equations Ek (b) of the form c1x1 + c2x2 + · · · + ck−1 xk−1 = xk + b, where b ∈ Z and ci ∈ Z+ for all i. We give universal upper bounds and qualified lower bounds for t-color Rado numbers r(Ek (b); t) in terms of r(Ek (0); t). The qualification is based on a new concept we name the excellence condition. We also give examples where the exact values of Rado numbers are obtained from these results.",

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AB - We consider Rado numbers of the regular equations Ek (b) of the form c1x1 + c2x2 + · · · + ck−1 xk−1 = xk + b, where b ∈ Z and ci ∈ Z+ for all i. We give universal upper bounds and qualified lower bounds for t-color Rado numbers r(Ek (b); t) in terms of r(Ek (0); t). The qualification is based on a new concept we name the excellence condition. We also give examples where the exact values of Rado numbers are obtained from these results.

KW - Experimental mathematics

KW - Ramsey theory

UR - https://www.scopus.com/pages/publications/85103395768

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EP - 10

JO - Discrete Mathematics Letters

JF - Discrete Mathematics Letters

ER -

Rado numbers of regular nonhomogeneous equations

Abstract

Keywords

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