{"paper":{"title":"Combinatorial positivity of translation-invariant valuations and a discrete Hadwiger theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.CO","authors_text":"Katharina Jochemko, Raman Sanyal","submitted_at":"2015-05-27T19:27:48Z","abstract_excerpt":"We introduce the notion of combinatorial positivity of translation-invariant valuations on convex polytopes that extends the nonnegativity of Ehrhart h*-vectors. We give a surprisingly simple characterization of combinatorially positive valuations that implies Stanley's nonnegativity and monotonicity of h*-vectors and generalizes work of Beck et al. (2010) from solid-angle polynomials to all translation-invariant simple valuations. For general polytopes, this yields a new characterization of the volume as the unique combinatorially positive valuation up to scaling. For lattice polytopes our re"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.07440","kind":"arxiv","version":4},"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"}