Year: 2025
Type: preprint
Abstract: A classical result in combinatorial number theory states that the largest subset of $[n]$ avoiding a solution to the equation $x+y=z$ is of size $\lceil n/2 \rceil$. For all integers $k>m$, we prove multicolored extensions of this result where we maximize the sum and product of the sizes of sets $A_1,A_2,\dots,A_k \subseteq [n]$ avoiding a rainbow solution to the Schur equation $x_1+x_2+\dots+x_m=x_{m+1}$. Moreover, we determine all the extremal families.
Source: arXiv (Cornell University)
Authors: Győri, Ervin, He, Zhen, Lv, Zequn, Salia, Nika, Tompkins, Casey, Varga, Kitti, Zhu, Xiutao
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4417539707
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