Non-central sections of the regular n-simplex
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866912204297601024 |
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| author | König, Hermann |
| author_facet | König, Hermann |
| contents | We show that the maximal non-central hyperplane sections of the regular n-simplex of side-length sqrt 2 at a fixed distance t to the centroid are those parallel to a face of the simplex, if $\sqrt{(n-2)/(3(n+1))} < t < \sqrt{(n-1)/(2(n+1))}$ and $n>4$. For $n=4$, the same is true in a slightly smaller range for t. This adds to a previous result for $\sqrt{(n-1)/(2(n+1))} < t < \sqrt{n/(n+1)}$. For $n=2,3$, we determine the maximal and the minimal sections for all distances t to the centroid. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2312_01325 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Non-central sections of the regular n-simplex König, Hermann Functional Analysis Combinatorics 52A38 We show that the maximal non-central hyperplane sections of the regular n-simplex of side-length sqrt 2 at a fixed distance t to the centroid are those parallel to a face of the simplex, if $\sqrt{(n-2)/(3(n+1))} < t < \sqrt{(n-1)/(2(n+1))}$ and $n>4$. For $n=4$, the same is true in a slightly smaller range for t. This adds to a previous result for $\sqrt{(n-1)/(2(n+1))} < t < \sqrt{n/(n+1)}$. For $n=2,3$, we determine the maximal and the minimal sections for all distances t to the centroid. |
| title | Non-central sections of the regular n-simplex |
| topic | Functional Analysis Combinatorics 52A38 |
| url | https://arxiv.org/abs/2312.01325 |