Shapley-Folkman-type Theorem for Integrally Convex Sets
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866914914362195968 |
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| author | Murota, Kazuo Tamura, Akihisa |
| author_facet | Murota, Kazuo Tamura, Akihisa |
| contents | The Shapley-Folkman theorem is a statement about the Minkowski sum of (non-convex) sets, expressing the closeness of the Minkowski sum to convexity in a quantitative manner. This paper establishes similar theorems for integrally convex sets, L-natural-convex sets, and M-natural-convex sets, which are major classes of discrete convex sets in discrete convex analysis. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_15125 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Shapley-Folkman-type Theorem for Integrally Convex Sets Murota, Kazuo Tamura, Akihisa Combinatorics 52A41, 90C27, 90C25 The Shapley-Folkman theorem is a statement about the Minkowski sum of (non-convex) sets, expressing the closeness of the Minkowski sum to convexity in a quantitative manner. This paper establishes similar theorems for integrally convex sets, L-natural-convex sets, and M-natural-convex sets, which are major classes of discrete convex sets in discrete convex analysis. |
| title | Shapley-Folkman-type Theorem for Integrally Convex Sets |
| topic | Combinatorics 52A41, 90C27, 90C25 |
| url | https://arxiv.org/abs/2305.15125 |