{"paper":{"title":"Tropical determinant on transportation polytope","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ivan Soprunov, Jenya Soprunova, Sailaja Gajula","submitted_at":"2014-10-13T17:23:31Z","abstract_excerpt":"Let ${\\mathcal D}^{k,l}(m,n)$ be the set of all the integer points in the transportation polytope of $kn\\times ln$ matrices with row sums $lm$ and column sums $km$. In this paper we find the sharp lower bound on the tropical determinant over the set ${\\mathcal D}^{k,l}(m,n)$. This integer piecewise-linear programming problem in arbitrary dimension turns out to be equivalent to an integer non-linear (in fact, quadratic) optimization problem in dimension two. We also compute the sharp upper bound on a modification of the tropical determinant, where the maximum over all the transversals in a matr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.3397","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"}