{"paper":{"title":"On a transport problem and monoids of non-negative integers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.GR","authors_text":"Aureliano M. Robles-P\\'erez, Jos\\'e Carlos Rosales","submitted_at":"2016-11-08T17:42:13Z","abstract_excerpt":"A problem about how to transport profitably a group of cars leads us to study the set $T$ formed by the integers $n$ such that the system of inequalities, with non-negative integer coefficients,\n  $$a_1x_1 +\\cdots+ a_px_p + \\alpha \\leq n \\leq b_1x_1 +\\cdots+ b_px_p - \\beta$$ has at least one solution in ${\\mathbb N}^p$. We will see that $T\\cup\\{0\\}$ is a submonoid of $({\\mathbb N},+)$. Moreover, we show algorithmic processes to compute $T$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.02627","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"}