{"paper":{"title":"Identifying Maximal Non-Redundant Integer Cone Generators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LO","authors_text":"Ruzica Piskac, Slobodan Mitrovi\\'c, Viktor Kun\\v{c}ak","submitted_at":"2019-03-20T15:55:48Z","abstract_excerpt":"A non-redundant integer cone generator (NICG) of dimension $d$ is a set $S$ of vectors from $\\{0,1\\}^d$ whose vector sum cannot be generated as a positive integer linear combination of a proper subset of $S$. The largest possible cardinality of NICG of a dimension $d$, denoted by $N(d)$, provides an upper bound on the sparsity of systems of integer equations with a large number of integer variables. A better estimate of $N(d)$ means that we can consider smaller sub-systems of integer equations when solving systems with many integer variables. Furthermore, given that we can reduce constraints o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.08571","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"}