A special balancing game, Victor Grinberg's question
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866929624690196480 |
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| author | Bárány, Imre |
| author_facet | Bárány, Imre |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_08238 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A special balancing game, Victor Grinberg's question Bárány, Imre Combinatorics Primary 52A15, secondary 91A05 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. |
| title | A special balancing game, Victor Grinberg's question |
| topic | Combinatorics Primary 52A15, secondary 91A05 |
| url | https://arxiv.org/abs/2412.08238 |