{
  "abstract": "We study integer-interval deformations of Coxeter arrangements of types $A$, $B$, and $D$, assigning an integer interval to each root direction through an integer-valued root function. We introduce a local compatibility condition on this root function. For compatible root functions, subject to additional local bounds in types $B$ and $D$, we derive characteristic-polynomial formulas as binomial sums over cyclic orders in type $A$ and signed permutations in types $B$ and $D$. The proofs use the finite-field method and reduce hyperplane avoidance to consecutive-gap inequalities. These formulas recover, in particular, the classical Catalan and Shi characteristic polynomials.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.29203",
  "author_total": 3,
  "authors": [
    {
      "name": "Yanru Chen"
    },
    {
      "name": "Ang Li"
    },
    {
      "name": "Suijie Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/c5ycwmgt3dc71.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.29203",
  "fulltext_url": null,
  "id": "c5ycwmgt3dc71",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.29203",
  "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": "W7204893074",
  "pdf_url": "https://arxiv.org/pdf/2608.29203",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/c5ycwmgt3dc71.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2608.29203",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.29203"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Interval Deformations of Coxeter Arrangements",
  "title_text": "Interval Deformations of Coxeter Arrangements",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/c5ycwmgt3dc71",
  "venue": "arXiv",
  "versions": []
}