{"paper":{"title":"Separations of Matroid Freeness Properties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Arnab Bhattacharyya, Elena Grigorescu, Jakob Nordstr\\\"om, Ning Xie","submitted_at":"2010-08-25T22:20:09Z","abstract_excerpt":"Properties of Boolean functions on the hypercube invariant with respect to linear transformations of the domain are among the most well-studied properties in the context of property testing. In this paper, we study the fundamental class of linear-invariant properties called matroid freeness properties. These properties have been conjectured to essentially coincide with all testable linear-invariant properties, and a recent sequence of works has established testability for increasingly larger subclasses. One question left open, however, is whether the infinitely many syntactically different pro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.4401","kind":"arxiv","version":2},"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"}