An Improved Upper Bound for Colorings Without Symmetrically Colored $k$-Term Arithmetic Progressions

Ruizhe Shi, Yiqi Dong

Given a coloring $c$ and an even $k\ge 4$, a nontrivial $k$-term arithmetic progression~($k$-AP) $a,a+d,\dots ,a+(k-1)d$ is called symmetrically colored if $c(a+(i-1)d)=c(a+(k-i)d)…