{"paper":{"title":"Axiomatizations of quasi-Lov\\'asz extensions of pseudo-Boolean functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Jean-Luc Marichal, Miguel Couceiro","submitted_at":"2010-11-29T17:23:56Z","abstract_excerpt":"We introduce the concept of quasi-Lov\\'asz extension as being a mapping $f\\colon I^n\\to\\R$ defined on a nonempty real interval $I$ containing the origin and which can be factorized as $f(x_1,...,x_n)=L(\\phi(x_1),...,\\phi(x_n))$, where $L$ is the Lov\\'asz extension of a pseudo-Boolean function $\\psi\\colon\\{0,1\\}^n\\to\\R$ (i.e., the function $L\\colon\\R^n\\to\\R$ whose restriction to each simplex of the standard triangulation of $[0,1]^n$ is the unique affine function which agrees with $\\psi$ at the vertices of this simplex) and $\\phi\\colon I\\to\\R$ is a nondecreasing function vanishing at the origin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.6302","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"}