{"paper":{"title":"On the number of points in a lattice polytope","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.CO","authors_text":"Arseniy Akopyan, Makoto Tagami","submitted_at":"2010-04-09T23:27:03Z","abstract_excerpt":"In this article we will show that for every natural $d$ and $n>1$ there exists a natural number $t$ such that for every $d$-dimensional simplicial complex $\\mathcal{T}$ with vertices in $\\mathbb{Z}^d$, the number of lattice points in the $t^{\\mathrm{th}}$ dilate of $\\mathcal{T}$ is exactly $\\chi(\\mathcal{T})$ modulo $n$, where $\\chi(\\mathcal{T})$ is the Euler characteristic of $\\mathcal{T}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.1661","kind":"arxiv","version":3},"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"}