{
  "abstract": "Multiple chessboard complexes are deleted joins of skeleta of a simplex. We classify their homotopy types for at most three rows and extend this classification to arbitrary column capacities, with the $2$-torus as the only exception to a wedge of spheres. We determine explicit homotopy decompositions for two families with four and five rows and use a common capacity redistribution map to construct infinite families with $2$- and $3$-torsion in integral homology. Together, these results give a negative answer to the Segre part of the problem posed by Reiner and Roberts on characteristic-free resolutions of Segre and Veronese modules and identify three as the largest number of rows for which all generalized chessboard complexes have torsion-free integral homology. Our $3$-torsion construction applies to every square ordinary chessboard complex with at least five rows. Combined with earlier results, it completes the proof of the Shareshian-Wachs conjecture on torsion in chessboard complexes.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.37827",
  "author_total": 2,
  "authors": [
    {
      "name": "Ivan Limonchenko"
    },
    {
      "name": "Seonghyeon Yu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ava3950g0w72a.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.37827",
  "fulltext_url": null,
  "id": "ava3950g0w72a",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.37827",
  "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.AT"
    ],
    [
      "arxiv",
      "math.CO"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.37827",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ava3950g0w72a.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.37827",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.37827"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.AT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Homotopy types and torsion in homology of generalized chessboard complexes",
  "title_text": "Homotopy types and torsion in homology of generalized chessboard complexes",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/ava3950g0w72a",
  "venue": "arXiv",
  "versions": []
}