2024/04/08 by Zhengxing Lian, Rongzhong Xiao, Lian, Zhengxing +1
Computer Science · Mathematics · #Coding theory and cryptography #Combinatorics (math.CO) #Dynamical Systems (math.DS) #FOS: Mathematics #Graph theory and applications #Limits and Structures in Graph Theory #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2404.05226
openalex publication_date 2024/04/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the paper, we search for monochromatic infinite additive structures involving polynomials over ℕ. It is proved that for any r∈ ℕ, any two distinct natural numbers a,b, and any 2-coloring of ℕ, there exist two sets B,C⊂ ℕ with |B|=r and |C|=∞ such that there exists some color containing B+aC and B+bC.