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.
Chernoff's Inequality - A very elementary proof
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abstract
We give a very simple proof of a strengthened version of Chernoff's Inequality. We derive the same conclusion from much weaker assumptions.
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math.CO 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
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The extensible no-$(k(n)+1)$-in-line problem
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.