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<p>We explore variants of the following open question: Split <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\([0,1]^2\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mo stretchy="false">[</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo stretchy="false">]</mo> </mrow> <mn>2</mn> </msup> </math></EquationSource> </InlineEquation> into <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(N^2\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>N</mi> <mn>2</mn> </msup> </math></EquationSource> </InlineEquation> squares with side length 1/<i>N</i>. Is there a way to select <i>N</i> of these squares such that each line intersects only <i>O</i>(1) of them?</p>

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On the N-set Occupancy Problem

  • 期刊论文

  • 发表日期：

    2025年11月16日

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  • Ciprian Demeter,
  • Ruixiang Zhang

摘要

We explore variants of the following open question: Split \([0,1]^2\) [ 0 , 1 ] 2 into \(N^2\) N 2 squares with side length 1/N. Is there a way to select N of these squares such that each line intersects only O(1) of them?