{"paper":{"title":"Multidimensional lower density versions of Pl\\\"unnecke's inequality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.CO","authors_text":"Kamil Bulinski","submitted_at":"2016-04-06T01:42:18Z","abstract_excerpt":"We investigate the lower asymptotic density of sumsets in $\\mathbb{N}^2$ by proving certain Pl\\\"unnecke type inequalities for various notions of lower density in $\\mathbb{N}^2$. More specifically, we introduce a notion of lower tableaux density in $\\mathbb{N}^2$ which involves averaging over convex tableaux-shaped regions in $\\mathbb{N}^2$ which contain the origin. This generalizes the well known Pl\\\"unnecke type inequality for the lower asymptotic density of sumsets in $\\mathbb{N}$. We also provide a conjectural Pl\\\"unnecke inequality for the more basic notion of lower rectangular asymtpotic "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.01462","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"}