Supplementary material for "Exact area thresholds for rectangle-free grid colourings"

This repository contains the supplementary material for the research article “Exact area thresholds for rectangle-free grid colourings”. The supplementary files provide computational certificates, construction data, and verification code supporting the computer-assisted results of the paper. In particular, they contain the explicit certificates used in the proof of Theorem 5.4 for rectangle-free grid colourings at the remaining finite heights not covered directly by the theoretical constructions. The archive includes: explicit combinatorial certificates represented as partitions of the row set; data for the computer-built rectangle-free colourings; programs used to construct the certificates; an independent verification program checking that the required partitions are valid, pairwise edge-disjoint in the corresponding graph representation, and yield rectangle-free colourings. The computational part complements the theoretical results based on counting bounds, equitable edge colourings, graph packings, resolvable designs, Kirkman and nearly Kirkman triple systems, and affine planes. The material is provided to ensure reproducibility and independent verification of the computer-assisted results presented in the article.