{
  "abstract": "Motivated by Kawanoue's construction of a basis for the derivation module of the cone of the extended Catalan arrangement of type $B_\\ell$, we construct an explicit basis for the derivation module of $\\mathbf{c}Shi(B_\\ell,m)$. Our construction generalizes the previously known case $m=1$ to $m\\geq1$. It also provides a partial answer to a question of Abe and Terao concerning explicit constructions of simple-root bases.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.17370",
  "author_total": 1,
  "authors": [
    {
      "name": "Zixuan Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2qbd7bct42v80.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.17370",
  "fulltext_url": null,
  "id": "2qbd7bct42v80",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.17370",
  "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.CO"
    ],
    [
      "openalex",
      "2607|Advanced Combinatorial Mathematics"
    ]
  ],
  "openalex": "W7213428097",
  "pdf_url": "https://arxiv.org/pdf/2609.17370",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2qbd7bct42v80.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:45Z",
      "native_id": "2609.17370",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.17370"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "On the extended Shi arrangement of type $B_{\\ell}$",
  "title_text": "On the extended Shi arrangement of type B_ℓ",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:45Z",
  "url": "https://research.draconitic.com/paper/2qbd7bct42v80",
  "venue": "arXiv",
  "versions": []
}