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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2507.13421 |
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| _version_ | 1866912490315579392 |
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| author | Soberón, Pablo |
| author_facet | Soberón, Pablo |
| contents | In this paper, we study the problem of splitting fairly bundles of items. We show that given $n$ bundles with $m$ kinds of items in them, it is possible to distribute the value of each kind of item fairly among $r$ persons by breaking apart at most $(r-1)m$ bundles. Moreover, we can guarantee that each participant will receive roughly $n/r - mr/2$ full bundles. The proof methods are topological and use a modified form of the configuration space/test map scheme. We obtain optimal results when $r$ is a power of two. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_13421 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fair distribution of bundles Soberón, Pablo Combinatorics Computer Science and Game Theory 91B32 F.2.2; J.4 In this paper, we study the problem of splitting fairly bundles of items. We show that given $n$ bundles with $m$ kinds of items in them, it is possible to distribute the value of each kind of item fairly among $r$ persons by breaking apart at most $(r-1)m$ bundles. Moreover, we can guarantee that each participant will receive roughly $n/r - mr/2$ full bundles. The proof methods are topological and use a modified form of the configuration space/test map scheme. We obtain optimal results when $r$ is a power of two. |
| title | Fair distribution of bundles |
| topic | Combinatorics Computer Science and Game Theory 91B32 F.2.2; J.4 |
| url | https://arxiv.org/abs/2507.13421 |