{
  "abstract": "We study min-plus Bruhat cells $B_{trop}^{(n)} \\odot p\\odot B_{trop}^{(n)}$, where $B_{trop}^{(n)}$ denotes the set of all upper-triangular matrices over $\\RR \\cup \\{\\infty\\}$, and $p$ is a permutation. It is proved that $\\dim (B_{trop}^{(n)} \\odot p \\odot B_{trop}^{(n)})= \\frac{n(n+1)}{2} + l(p)$, where $l(p)$ is the length of $p$ in Coxeter generators. Also we provide an explicit description of the cell $B_{trop}^{(n)}(\\RR) \\odot p_0\\odot B_{trop}^{(n)}(\\RR)$ (up to a subset of dimension less than $n^2$) for the highest in Bruhat order permutation $p_0$. Finally, it is shown that for a tropically non-singular matrix $A$ for at most one permutation $p_A$ it can hold $A\\in B_{trop}^{(n)}\\odot p_A\\odot B_{trop}^{(n)}$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.03896",
  "author_total": 1,
  "authors": [
    {
      "name": "Dima Grigoriev"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7xq5vj2666w92.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.03896",
  "fulltext_url": null,
  "id": "7xq5vj2666w92",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.03896",
  "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.AG"
    ],
    [
      "arxiv",
      "math.CO"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.03896",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7xq5vj2666w92.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T15:21:29Z",
      "native_id": "2611.03896",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.03896"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Min-plus Bruhat decomposition",
  "title_text": "Min-plus Bruhat decomposition",
  "type": "preprint",
  "updated_at": "2026-11-06T18:21:01Z",
  "url": "https://research.draconitic.com/paper/7xq5vj2666w92",
  "venue": "arXiv",
  "versions": []
}