{
  "abstract": "We describe a mixed subdivision of the $(n-1)$-dimensional Loday associahedron into $(n-1)!$ maximal cells which are combinatorial cubes, and we show that the face poset of this subdivision is isomorphic to the face poset of the subdivision of the $1\\times 2\\times \\dotsb \\times (n-1)$ box into unit cubes. More generally, we describe mixed subdivisions of generalized associahedra into pieces which are Minkowski sums of Bruhat interval polytopes. Our subdivisions arise from a torus-equivariant embedded (in a product of flag varieties) degeneration of brick varieties into reduced unions of products of Richardson varieties. The subdivision of Loday's associahedron allows us to `embed' the 1-skeleton of the permutahedron in the boundary of the associahedron.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.23004",
  "author_total": 2,
  "authors": [
    {
      "name": "Raj Gandhi"
    },
    {
      "name": "Gabe Udell"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bzcwx7e68gkjb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.23004",
  "fulltext_url": null,
  "id": "bzcwx7e68gkjb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.23004",
  "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.AG"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "2607|Advanced Combinatorial Mathematics"
    ]
  ],
  "openalex": "W7222935534",
  "pdf_url": "https://arxiv.org/pdf/2610.23004",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bzcwx7e68gkjb.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:37Z",
      "native_id": "2610.23004",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.23004"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "A cubulation of the associahedron using a torus-equivariant degeneration of the brick variety",
  "title_text": "A cubulation of the associahedron using a torus-equivariant degeneration of the brick variety",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:31Z",
  "url": "https://research.draconitic.com/paper/bzcwx7e68gkjb",
  "venue": "arXiv",
  "versions": []
}