{"paper":{"title":"Transversal Difference Numbers in Finite Abelian Quotients","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.CR","cs.DM","math.CO"],"primary_cat":"math.NT","authors_text":"George C. \\c{T}urca\\c{s}, Mugurel Barcau, Vicen\\c{t}iu Pa\\c{s}ol","submitted_at":"2026-06-26T11:03:47Z","abstract_excerpt":"Given \\(H\\leq G\\) finite abelian groups, a transversal \\(T\\subseteq G\\) for \\(G/H\\) has fixed size \\(|G/H|\\), but its ambient difference support \\(D(T)=T-T\\) can vary with the embedding of \\(H\\) in \\(G\\). We call $ \\delta(G,H)=\\min_T |D(T)| $ the transversal difference number of the pair \\((G,H)\\). This invariant is related to finite abelian factorisation, tiling complements, and small-sumset questions, and is motivated by recent work regarding ambient Galois labels in CRT transforms for cyclotomic-subfield homomorphic encryption. We prove various results regarding this invariant, including a "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.27961","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.27961/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}