{"paper":{"title":"Optimal transport and integer partitions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.OC"],"primary_cat":"math.NT","authors_text":"Sonja Hohloch","submitted_at":"2017-04-05T23:14:11Z","abstract_excerpt":"We link the theory of optimal transportation to the theory of integer partitions. Let $\\mathscr P(n)$ denote the set of integer partitions of $n \\in \\mathbb N$ and write partitions $\\pi \\in \\mathscr P(n)$ as $(n_1, \\dots, n_{k(\\pi)})$. Using terminology from optimal transport, we characterize certain classes of partitions like symmetric partitions and those in Euler's identity\n  $|\\{ \\pi \\in \\mathscr P(n) |$ all $ n_i $ distinct $ \\} | = | \\{ \\pi \\in \\mathscr P(n) | $ all $ n_i $ odd $ \\}|$.\n  Then we sketch how optimal transport might help to understand higher dimensional partitions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.01666","kind":"arxiv","version":1},"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"}