On the Geometry of the Birkhoff Polytope. I. The operator $\ell^p_n$-norms
The geometry of the Birkhoff polytope, i.e., the compact convex set of all $n \times n$ doubly stochastic matrices, has been an active subject of research. While its faces, edges and facets as well as its volume have been intensely studied, other geometric characteristics such as the center and radi...
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| Main Authors | , , |
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| Format | Journal Article |
| Language | English |
| Published |
21.10.2023
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| Subjects | |
| Online Access | Get full text |
| DOI | 10.48550/arxiv.2310.14041 |
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| Summary: | The geometry of the Birkhoff polytope, i.e., the compact convex set of all $n
\times n$ doubly stochastic matrices, has been an active subject of research.
While its faces, edges and facets as well as its volume have been intensely
studied, other geometric characteristics such as the center and radius were
left off, despite their natural uses in some areas of mathematics. In this
paper, we completely characterize the Chebyshev center and the Chebyshev radius
of the Birkhoff polytope associated with the metrics induced by the operator
$\ell^p_n$-norms for the range $1 \leq p \leq \infty$. |
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| DOI: | 10.48550/arxiv.2310.14041 |