{"paper":{"title":"Discrete Envy-free Division of Necklaces and Maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Amanda Ruiz, Francis Edward Su, Kathryn Nyman, Roberto Barrera, Yan X. Zhang","submitted_at":"2015-10-07T21:04:00Z","abstract_excerpt":"We study the discrete variation of the classical cake-cutting problem where n players divide a 1-dimensional cake with exactly (n-1) cuts, replacing the continuous, infinitely divisible \"cake\" with a necklace of discrete, indivisible \"beads.\" We focus specifically on envy-free divisions, exploring different constraints on player-preferences. We show we usually cannot guarantee an envy-free division and consider situations where we can obtain an envy-free division for relatively small. We also prove a 2-dimensional result with a grid of indivisible objects. This may be viewed as a way to divide"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.02132","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}