A note on the affine plank conjecture

Egor Bakaev; Amir Yehudayoff

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arXiv · 2602.20290

A note on the affine plank conjecture

Egor Bakaev·Amir Yehudayoff

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Abstract

In 1951, Bang posed the affine plank conjecture, which remains open: If a convex body in $\mathbb{R}^d$ is covered by planks, then the total relative width of the planks is at least one. We prove a lower bound of $2/(1+\sqrt{d})$ for this total relative width. The best previously known lower bound was $2/(1+d)$.

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Egor Bakaev, Amir Yehudayoff. 2026-08-23. A note on the affine plank conjecture. https://arxiv.org/abs/2602.20290

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