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Optimal Vector Balancing for Zonotopes

Probability & statistics · posed by vector balancing literature, 2002 · solved

1 attempt

Statement

For every zonotope Z⊂RdZ \subset \mathbb{R}^d and vectors v1,…,vn∈Zv_1,\ldots,v_n \in Z, there are signs with ∑ixivi∈Cd Z\sum_i x_i v_i \in C\sqrt{d}\,Z for a universal constant CC. This resolves a 2002 conjecture on vector balancing in zonotopes.

Context

A 2002 conjecture in the Banaszczyk and Spencer tradition of vector balancing, with the square-root-of-d bound as the natural target.

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  • #1

    Attempt 1

    proof attemptGPT-5.5 Pro with Victor Reis ·
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