{
  "abstract": "A quiver representation consists of a collection of vector spaces along with a set of arrows, which are linear maps between these spaces. In this work, we study quiver representations in equioriented type $A$ which are also chain complexes; that is, in which consecutive arrows compose to zero. We show that orbits of these representations under a change of basis action are in bijection with mixed dimer covers of a $2 \\times n$ grid graph. The latter object can be endowed with a partial order which is a distributive lattice, and we show that the degeneration order on the orbits of chain complexes is a coarsening of this partial order. In addition, we use recent matrix formulae of Claussen and Ovenhouse to enumerate these orbits. This also computes the Kostant partition function applied to height-restricted, type $A$ roots. When the dimension vector is uniform, we discuss a correspondence with paths of a beam of light bouncing between glass plates and give an explicit generating function.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.00202",
  "author_total": 6,
  "authors": [
    {
      "name": "Portia X. Anderson"
    },
    {
      "name": "Esther Banaian"
    },
    {
      "name": "Melanie J. Ferreri"
    },
    {
      "name": "Nicholas Mayers"
    },
    {
      "name": "Shiyun Wang"
    },
    {
      "name": "Alexander N. Wilson"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/20wqnn4cb2cdw.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.00202",
  "fulltext_url": null,
  "id": "20wqnn4cb2cdw",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.00202",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "2608|Algebraic structures and combinatorial models"
    ]
  ],
  "openalex": "W7206202348",
  "pdf_url": "https://arxiv.org/pdf/2609.00202",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/20wqnn4cb2cdw.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:04Z",
      "native_id": "2609.00202",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.00202"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Varieties of chain complexes and mixed dimer covers",
  "title_text": "Varieties of chain complexes and mixed dimer covers",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:04Z",
  "url": "https://research.draconitic.com/paper/20wqnn4cb2cdw",
  "venue": "arXiv",
  "versions": []
}