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arXiv · 2412.08238

A special balancing game, Victor Grinberg's question

Imre Bárány
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Abstract

In a vector balancing game, on step $k$ player 1 chooses a unit vector $v_k$ and player 2 chooses a sign $\varepsilon_k\in \{-1,1\}$, and the position after $n$ steps is $z_n=\sum_1^n\varepsilon_k v_k$. Player 1's target is to make $\|z_n\|$ large and player 2's target is to make it small. We consider a special case of this game.

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Imre Bárány. 2024-12-11. A special balancing game, Victor Grinberg's question. https://arxiv.org/abs/2412.08238

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