{"paper":{"title":"On the set of catenary degrees of finitely generated cancellative commutative monoids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Christopher O'Neill, Gautam Webb, Reuben Tate, Vadim Ponomarenko","submitted_at":"2015-06-25T00:43:09Z","abstract_excerpt":"The catenary degree of an element $n$ of a cancellative commutative monoid $S$ is a nonnegative integer measuring the distance between the irreducible factorizations of $n$. The catenary degree of the monoid $S$, defined as the supremum over all catenary degrees occurring in $S$, has been heavily studied as an invariant of nonunique factorization. In this paper, we investigate the set $\\mathsf C(S)$ of catenary degrees achieved by elements of $S$ as a factorization invariant, focusing on the case where $S$ in finitely generated (where $\\mathsf C(S)$ is known to be finite). Answering an open qu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.07587","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"}