{
  "abstract": "Totally equimodular matrices generalize totally unimodular matrices and arise in the theory of box-total dual integrality. We prove that every nonempty pointed polyhedron admitting a rational totally equimodular description has combinatorial diameter at most 8d 3 (1 + 2 log d), where d is its intrinsic dimension. The bound is independent of the number of inequalities, the right-hand side, and the magnitudes of subdeterminants, it applies to unbounded and degenerate polyhedra, and it matches the best asymptotic bound known for totally unimodular matrices. This resolves a question raised by Lancini and Pisanu. We also give a sharp upper bound 2d 2 on the number of facets of a d-dimensional totally equimodular polytope. Finally, we show that a shadowsimplex algorithm uses O(d 4 log d) expected optimization pivots from a feasible basis on full-dimensional pointed polyhedra, and O(md 4 log d) expected feasibility pivots for descriptions with m inequalities and full column rank.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "name": "Emiliano Lancini"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/82q4nh83r6jxx.bib",
  "cited_by": 0,
  "doi": null,
  "fulltext_url": null,
  "id": "82q4nh83r6jxx",
  "issns": [],
  "landing_url": "https://hal.science/hal-05849014v1",
  "language": "en",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "hal",
      "0.info"
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      "hal",
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  "openalex": null,
  "pdf_url": "https://hal.science/hal-05849014/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/82q4nh83r6jxx.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:20:18Z",
      "native_id": "hal-05849014",
      "source": "hal",
      "url": "https://hal.science/hal-05849014v1"
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  "subjects": [
    {
      "field": "mathematics",
      "origin": "hal:1.math.math-co",
      "subfield": "combinatorics"
    }
  ],
  "title": "Totally Equimodular Polyhedra: Diameters and Pivots",
  "title_text": "Totally Equimodular Polyhedra: Diameters and Pivots",
  "type": "preprint",
  "updated_at": "2026-11-04T12:20:49Z",
  "url": "https://research.draconitic.com/paper/82q4nh83r6jxx",
  "venue": "HAL",
  "versions": []
}