3 problems

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Conjecture that the unit-ball decomposition constant is not sharp
Let $B^n=\{x\in\mathbb{R}^n:\|x\|\leq 1\}$ be the unit $n$ -ball. A decomposition of $B^n$ is a collection of sets whose union is $B^n$ ; the pieces have diameter less than…
Conjectureopendecompositions geometric-topologyarXiv posted 2 days ago
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Probabilistic $(1,3/2)$ -decomposability conjecture for random matroids
Probabilistic $(1,3/2)$ -decomposability conjecture. With high probability as $n\to\infty$ , the random matroid on ground set $[n]$ is $(1,3/2)$ -decomposable.
Conjecturerefuteddecompositions matroid-theory random-matroidsarXiv posted 2 days ago
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Bérczi–Schwarcz–Yamaguchi's universal $(1,2)$ -decomposability conjecture for matroids
Bérczi–Schwarcz–Yamaguchi's conjecture. Every matroid is $(1,2)$ -decomposable.
Conjecturerefuteddecompositions finite-geometries matroid-theoryarXiv posted 2 days ago

Conjecture that the unit-ball decomposition constant is not sharp