{
  "abstract": "Let $W=W(B_n)$ act diagonally on $\\mathfrak{h}\\oplus\\mathfrak{h}^*$, let $S=\\mathbb{C}[\\mathfrak{h}\\oplus\\mathfrak{h}^*]$, let $J\\subset S$ be the ideal generated by the $W$-alternating polynomials and $\\mathfrak{m}_S$ is the maximal ideal of the origin. For sufficiently large $m$ we compute $q,t$-Fuss-Catalan polynomial $Cat^{(m)}(B_n;q,t):=Hilb(\\frac{J^m}{\\mathfrak{m}_S J^m})_{det-part}$ and imply $Cat^{(m)}(B_n;1,1)=\\binom{n(m+1)}{n}$. For proofs, we work with the $Γ$-equivariant Hilbert scheme $Y_n=nΓ$-$Hilb(\\mathbb{C}^2)$, $Γ=μ_2$ and Haiman-type Koszul complex that defines the punctual locus of $Y_n$. Our formula for $Cat^{(m)}(B_n;q,t)$ is derived from a localization computaion for the Haiman-type Koszul complex.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.11691",
  "author_total": 1,
  "authors": [
    {
      "name": "Alexei Oblomkov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5w5zp5snw0165.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.11691",
  "fulltext_url": null,
  "id": "5w5zp5snw0165",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.11691",
  "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": "W7212232568",
  "pdf_url": "https://arxiv.org/pdf/2609.11691",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5w5zp5snw0165.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:07Z",
      "native_id": "2609.11691",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.11691"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Asymptotic $q,t$-Fuss--Catalan numbers for type $B$",
  "title_text": "Asymptotic q,t-Fuss--Catalan numbers for type B",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:07Z",
  "url": "https://research.draconitic.com/paper/5w5zp5snw0165",
  "venue": "arXiv",
  "versions": []
}