Year: 2018
Type: preprint
Abstract: Let $r$ and $k$ be positive integers with $r \mid k$. Denote by $S_{\mathrm{\mathfrak{z}}}(k;r)$ the minimum integer $n$ such that every coloring $χ:[1,n] \rightarrow \{0,1,\dots,r-1\}$ admits a solution to $\sum_{i=1}^{k-1} x_i = x_k$ with $\sum_{i=1}^{k} χ(x_i) \equiv 0 \,(\mathrm{mod }\,r)$. We give some formulas and lower bounds for various instances.
Source: arXiv (Cornell University)
Author: Robertson, Aaron
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2787063168