{"paper":{"title":"Combinatorial rigidity of Incidence systems and Application to Dictionary learning","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Meera Sitharam, Menghan Wang, Mohamad Tarifi","submitted_at":"2016-03-14T01:40:40Z","abstract_excerpt":"Given a hypergraph $H$ with $m$ hyperedges and a set $Q$ of $m$ \\emph{pinning subspaces}, i.e.\\ globally fixed subspaces in Euclidean space $\\mathbb{R}^d$, a \\emph{pinned subspace-incidence system} is the pair $(H, Q)$, with the constraint that each pinning subspace in $Q$ is contained in the subspace spanned by the point realizations in $\\mathbb{R}^d$ of vertices of the corresponding hyperedge of $H$. This paper provides a combinatorial characterization of pinned subspace-incidence systems that are \\emph{minimally rigid}, i.e.\\ those systems that are guaranteed to generically yield a locally "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.04109","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"}