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Roth, Karl F · 1951 · DOI 10.1112/jlms/s1-26.3.198

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The extensible no-$(k(n)+1)$-in-line problem

math.CO · 2026-06-01 · unverdicted · novelty 6.0

Introduces the extensible no-(k(n)+1)-in-line problem on infinite grids, constructs optimal sets for linear k(n) and positive-density sets for power k(n), proves any high-density configuration requires k(n) growing polynomially, and reduces the constant-k case to regular functions.

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  • The extensible no-$(k(n)+1)$-in-line problem math.CO · 2026-06-01 · unverdicted · none · ref 13

    Introduces the extensible no-(k(n)+1)-in-line problem on infinite grids, constructs optimal sets for linear k(n) and positive-density sets for power k(n), proves any high-density configuration requires k(n) growing polynomially, and reduces the constant-k case to regular functions.