{
  "abstract": "We consider the integer version of Alkan--Gale's model on stability in a two-sided market, called the stable generalized allocation one. It is given by a triple $(G,b,C)$, where $G=(V,E)$ is a finite bipartite graph with nonnegative integer capacities $b(e)\\in{\\mathbb Z}_+$ of edges $e\\in E$, and for each vertex (``agent'') $v\\in V$, the preferences on the set $E_v$ of its incident edges depend on a choice function $C_v$. The latter acts on the set of vectors in ${\\mathbb Z}_+^{E_v}$ bounded by the capacities and obeys the standard axioms of substitutability and size monotonicity. Alkan--Gale's prominent theorem implies that the stability problem in this case always has a stable solution $x\\in{\\mathbb Z}_+^E$ and, moreover, the set ${\\cal S}_{G,b,C}$ of these solutions (``stable generalized allocations'') forms a distributive lattice. However, this lattice is rather intricate to construct and work with, and we wonder whether it can be represented via a ``simpler'' stability model. Answering this issue, we arrange a sort of splitting techniques to embed ${\\cal S}_{G,b,C}$, as a sublattice, in the lattice of stable matchings and, more compactly, in the lattice of stable allocations (as in Baiou--Balinski's stability model). This generalizes Fleiner's result on a detachment in the special case with all-unit capacities. Keywords: stable marriage, stable allocation, choice function, rotation, distributive lattice, poset representation",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.24581",
  "author_total": 1,
  "authors": [
    {
      "name": "Alexander V. Karzanov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/77gkc7j4xe89m.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.24581",
  "fulltext_url": null,
  "id": "77gkc7j4xe89m",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.24581",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "2002|Game Theory and Voting Systems"
    ]
  ],
  "openalex": "W7214044794",
  "pdf_url": "https://arxiv.org/pdf/2609.24581",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/77gkc7j4xe89m.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.24581",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.24581"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "On splitting properties of the stability problem with integer choice functions",
  "title_text": "On splitting properties of the stability problem with integer choice functions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/77gkc7j4xe89m",
  "venue": "arXiv",
  "versions": []
}