Extreme points of general transportation polytopes
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866909182066688000 |
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| author | Koehl, Patrice |
| author_facet | Koehl, Patrice |
| contents | Transportation matrices are $m\times n$ non-negative matrices whose row sums and row columns are equal to, or dominated above with given integral vectors $R$ and $C$. Those matrices belong to a convex polytope whose extreme points have been previously characterized. In this article, a more general set of non-negative transportation matrices is considered, whose row sums are bounded by two integral non-negative vectors $R_{min}$ and $R_{max}$ and column sums are bounded by two integral non-negative vectors $C_{min}$ and $C_{max}$. It is shown that this set is also a convex polytope whose extreme points are then fully characterized. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_16791 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Extreme points of general transportation polytopes Koehl, Patrice Combinatorics 05C50 G.2.1 Transportation matrices are $m\times n$ non-negative matrices whose row sums and row columns are equal to, or dominated above with given integral vectors $R$ and $C$. Those matrices belong to a convex polytope whose extreme points have been previously characterized. In this article, a more general set of non-negative transportation matrices is considered, whose row sums are bounded by two integral non-negative vectors $R_{min}$ and $R_{max}$ and column sums are bounded by two integral non-negative vectors $C_{min}$ and $C_{max}$. It is shown that this set is also a convex polytope whose extreme points are then fully characterized. |
| title | Extreme points of general transportation polytopes |
| topic | Combinatorics 05C50 G.2.1 |
| url | https://arxiv.org/abs/2404.16791 |