{"ID":2893567,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2507.13421","arxiv_id":"2507.13421","title":"Fair distribution of bundles","abstract":"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.","short_abstract":"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...","url_abs":"https://arxiv.org/abs/2507.13421","url_pdf":"https://arxiv.org/pdf/2507.13421v1","authors":"[\"Pablo Soberón\"]","published":"2025-07-17T14:46:42Z","proceeding":"math.CO","tasks":"[\"math.CO\",\"cs.GT\"]","methods":"[]","has_code":false}