{"paper":{"title":"Total positivity, Grassmannian and modified Bessel functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Alexey Glutsyuk, Victor Buchstaber","submitted_at":"2017-08-07T15:10:08Z","abstract_excerpt":"A rectangular matrix is called totally positive, if all its minors are positive. A point of a real Grassmanian manifold $G_{l,m}$ of $l$-dimensional subspaces in $\\mathbb R^m$ is called strictly totally positive, if one can normalize its Pl\\\"ucker coordinates to make all of them positive. The totally positive matrices and the subsets of strictly totally positive points in Grassmanian manifolds arise in many domains of mathematics, mechanics and physics. F.R.Gantmacher and M.G.Krein considered totally positive matrices in the context of classical mechanics. Total positivity was used for constru"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.02154","kind":"arxiv","version":3},"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"}