{"paper":{"title":"Homometry and direct-sum decompositions of lattice-convex sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.MG","authors_text":"Barbara Langfeld, Gennadiy Averkov","submitted_at":"2014-12-23T14:58:18Z","abstract_excerpt":"Two sets in $\\mathbb{R}^d$ are called homometric if they have the same covariogram, where the covariogram of a finite subset $K$ of $\\mathbb{R}^d$ is the function associating to each $u \\in \\mathbb{R}^d$ the cardinality of $K \\cap (K+u)$. Understanding the structure of homometric sets is important for a number of areas of mathematics and applications.\n  If two sets are homometric but do not coincide up to translations and point reflections, we call them nontrivially homometric. We study nontrivially homometric pairs of lattice-convex sets, where a set $K$ is called lattice-convex with respect "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.7676","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"}