Ordered Ramsey numbers of nested matchings versus triangles

Determine a precise formula for $R_<(NM^<_k,K^<_3)$ for every positive integer $k$.

Background

Known bounds place the ordered Ramsey number of a nested matching against an ordered triangle between linear expressions with different coefficients. A previously conjectured exact formula was disproved for k≥6k\ge6, and the survey notes that no precise formula is currently known.

References

Despite this progress, no precise formula for $R_<(NM_k, K<_3)$ is known.

— A Survey on Ordered Ramsey Numbers  (2502.02155 - Balko, 4 Feb 2025) in Subsubsection “Nested Matchings”