{"paper":{"title":"Lattice multi-polygons","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.MG"],"primary_cat":"math.CO","authors_text":"Akihiro Higashitani, Mikiya Masuda","submitted_at":"2012-03-31T09:17:00Z","abstract_excerpt":"We discuss generalizations of some results on lattice polygons to certain piecewise linear loops which may have a self-intersection but have vertices in the lattice $\\mathbb{Z}^2$. We first prove a formula on the rotation number of a unimodular sequence in $\\mathbb{Z}^2$. This formula implies the generalized twelve-point theorem in [12]. We then introduce the notion of lattice multi-polygons which is a generalization of lattice polygons, state the generalized Pick's formula and discuss the classification of Ehrhart polynomials of lattice multi-polygons and also of several natural subfamilies o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.0088","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"}