{"paper":{"title":"Factorization invariants in half-factorial affine semigroups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Alfredo S\\'anchez-R.-Navarro, Ignacio Ojeda, Pedro A. Garc\\'ia-S\\'anchez","submitted_at":"2012-07-24T21:51:14Z","abstract_excerpt":"Let $\\mathbb{N} \\mathcal{A}$ be the monoid generated by $\\mathcal{A} = {\\mathbf{a}_1, ..., \\mathbf{a}_n} \\subseteq \\mathbb{Z}^d.$ We introduce the homogeneous catenary degree of $\\mathbb{N} \\mathcal{A}$ as the smallest $N \\in \\mathbb N$ with the following property: for each $\\mathbf{a} \\in \\mathbb{N} \\mathcal{A}$ and any two factorizations $\\mathbf{u}, \\mathbf{v}$ of $\\mathbf{a}$, there exists factorizations $\\mathbf{u} = \\mathbf{w}_1, ..., \\mathbf{w}_t = \\mathbf{v} $ of $\\mathbf{a}$ such that, for every $k, \\mathrm{d}(\\mathbf{w}_k, \\mathbf{w}_{k+1}) \\leq N,$ where $\\mathrm{d}$ is the usual di"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.5838","kind":"arxiv","version":1},"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"}