{"paper":{"title":"Semigroups with fixed multiplicity and embedding dimension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.AC","authors_text":"A. Vigneron-Tenorio, D. Mar\\'in-Arag\\'on, J. C. Rosales, J. I. Garc\\'ia-Garc\\'ia, M. A. Moreno-Fr\\'ias","submitted_at":"2017-10-10T11:42:06Z","abstract_excerpt":"Given $m\\in \\mathbb{N},$ a numerical semigroup with multiplicity $m$ is called packed numerical semigroup if its minimal generating set is included in $\\{m,m+1,\\ldots, 2m-1\\}.$ In this work, packed numerical semigroups are used to built the set of numerical semigroups with fixed multiplicity and embedding dimension, and to create a partition in this set. Moreover, Wilf's conjecture is checked in the tree associated to some packed numerical semigroups."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.03523","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"}