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Creators/Authors contains: "Fiedler, Jacob B"

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  1. ; (, Journal of Fractal Geometry, Mathematics of Fractals and Related Topics)
    LetE \subseteq \mathbb{R}^{n}be a union of line segments andF \subseteq \mathbb{R}^{n}the set obtained fromEby extending each line segment inEto a full line. Keleti’sline segment extension conjectureposits that the Hausdorff dimension ofFshould equal that ofE. Working in\mathbb{R}^{2}, we use effective methods to prove a strong packing dimension variant of this conjecture. Furthermore, a key inequality in this proof readily entails the planar case of the generalized Kakeya conjecture for packing dimension. This is followed by several doubling estimates in higher dimensions and connections to related problems. 
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    Free, publicly-accessible full text available March 7, 2026