{"paper":{"title":"On multistochastic Monge-Kantorovich problem, bitwise operations, and fractals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Alexander P. Zimin, Alexander V. Kolesnikov, Nikita A. Gladkov","submitted_at":"2018-03-28T08:02:03Z","abstract_excerpt":"The multistochastic $ (n,k)$-Monge--Kantorovich problem on a product space $\\prod_{i=1}^n X_i$ is an extension of the classical Monge--Kantorovich problem. This problem is considered on the space of measures with fixed projections onto $X_{i_1} \\times \\ldots \\times X_{i_k}$ for all $k$-tuples $\\{i_1, \\ldots, i_k\\} \\subset \\{1, \\ldots, n\\}$ for a given $1 \\le k < n$. In our paper we study well-posedness of the primal and the corresponding dual problem. Our central result describes a solution $\\pi$ to the following important model case: $n=3, k=2, X_i = [0,1]$, the cost function $c(x,y,z) = xyz$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.10447","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"}