{
  "annotation_id": "7dd90409-1fc3-46ac-98f6-8908edf60183",
  "date_created": "2026-02-17T05:53:23.008000Z",
  "date_modified": "2026-02-17T05:53:23.008000Z",
  "file_hash": "a1501352c21348aff18b4557b26364c056100fea3cc64fb154ff715d99cbb9b8",
  "private": false,
  "record": {
    "abstract": "Deltoids provide a natural framework for studying defective (partial) matchings in abelian groups, and we develop both structure and existence results in this setting. Given finite subsets $A$ and $B$ of an abelian group $G$, a matching is a bijection $f:A\\to B$ such that $af(a)\\notin A$ for all $a\\in A$, a definition motivated by the study of canonical forms for symmetric tensors. We provide necessary and sufficient conditions for the existence of a partial matching with any prescribed defect, and then describe the minimal unavoidable defect for a pair $(A,B)$. We also define and examine a defective version of Chowla sets in the matching context. We prove a structure theorem identifying obstructions to the existence of partial matchings with small defect. Finally, within the deltoid setup, we establish max-min results on the partitioning of $A$ and $B$ into left- and right-admissible sets. Our tools mix results from transversal theory with ideas from additive number theory.",
    "arxiv_id": "2601.09774",
    "authors": [
      "Mohsen Aliabadi",
      "Jozsef Losonczy"
    ],
    "categories": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "Structure and Decomposition of Deltoids in Abelian Groups",
    "url": "https://arxiv.org/abs/2601.09774",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "a7780d4b-6354-49e2-aec6-872fc390f228",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}