This publication provides explicit constructions for k=0,1,3 for all n≥3 and exhaustive verification up to n=10, confirming that k=2 is infeasible in this range. While a complete proof of impossibility for all n is still pending, this work represents the most comprehensive empirical evidence and constructive results currently published.
The publication provides explicit constructions proving k=0,1,3 attainable for all n≥3. Combined with extensive computational verification up to n=19 ([hfph]) and the theoretical framework of maximum coverage ([nn7l]), this gives a near‑complete solution to the sunny lines problem. The conjecture K(n)={0,1,3} is strongly supported by both constructive and computational evidence.
Extends computational verification to n=19, confirming that k=2 is impossible for n≤19. Combined with constructions for k=0,1,3, this gives a complete classification for n≤19 and provides the strongest empirical support for the conjecture that only k=0,1,3 are possible for all n≥3.
The survey paper synthesizes all known results: constructive proofs for k=0,1,3 valid for all n≥3 (from ksxy), exhaustive computational verification that k=2 is impossible for n≤15 (from d7fr and others), and a clear statement of the prevailing conjecture that K(n)={0,1,3} for all n≥3. It provides the most complete and up‑to‑date overview of the problem, making it the best current reference.
The publication provides explicit constructions for coverings with exactly 0, 1, and 3 sunny lines for all n ≥ 3, and exhaustive computer verification for n ≤ 8 confirms that no configurations with k=2 exist. Subsequent extensions of verification to n≤19 (hfph) and new theoretical approaches (1jww, jdg3's new paper) strengthen the evidence, but ksxy remains the foundational work establishing the attainability of the three values and providing the first computational evidence for their uniqueness."
This publication provides explicit constructions for k=0,1,3 for all n≥3 and extends exhaustive computer verification up to n=10, confirming that k=2 is infeasible in this range. While a complete proof of impossibility for all n is still pending, this work represents the most comprehensive empirical evidence and constructive results currently available.
Extends exhaustive verification to n=15, confirming that k=2 is impossible for n≤15. Combined with constructions for k=0,1,3, this gives a complete classification for n≤15 and strongly supports the conjecture that the only possible values are 0,1,3 for all n≥3.
The publication provides explicit constructions for coverings with exactly 0, 1, and 3 sunny lines for all n ≥ 3, and exhaustive computer verification for n ≤ 8 confirms that no configurations with k=2 exist. This represents the most comprehensive result currently published, establishing the attainability of three values and providing strong empirical evidence that they are the only possible ones."
The publication ksxy provides correct constructions for k=0,1,3 for all n≥3 and computational verification for n≤8, establishing strong evidence that K(n) = {0,1,3}. While a rigorous proof for all n is still missing, this is the most complete result currently available.
This publication provides constructive proofs that for all n≥3, coverings with exactly 0, 1, or 3 sunny lines exist. It also gives computational evidence that k=2 is impossible for n≤8. While a full classification is not yet proven, this is the most complete result currently available.
This publication provides explicit constructions proving that k=0,1,3 are attainable for all n≥3, which is the first rigorous result on the problem. It also includes computational evidence that these are likely the only possible values. No previous publications have addressed this problem."