Intuitive norms are Euclidean

Shay Moran; Alexander Shlimovich; Amir Yehudayoff

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arXiv · 2501.02561

Intuitive norms are Euclidean

Shay Moran·Alexander Shlimovich·Amir Yehudayoff

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Abstract

We call a norm on $\mathbb{R}^n$ intuitive if for every points $p_1,\ldots,p_m$ in $\mathbb{R}^n$, one of the geometric medians of the points over the norm is in their convex hull. We characterize all intuitive norms.

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Shay Moran, Alexander Shlimovich, Amir Yehudayoff. 2025-01-07. Intuitive norms are Euclidean. https://arxiv.org/abs/2501.02561

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