{
  "abstract": "We prove the sign-isotypic components of the coinvariant rings $R_n^{(2,1)}$ and $R_n^{(2,0)} \\otimes R_n^{(0,1)}$ are isomorphic and show that the triply-graded multiplicity of this sign character is the Schröder polynomial $S_n(q,t,a)$, divided by $1+a$. This settles the sign-character component of a conjecture of Zabrocki (2019) on a module for the Delta theorem and proves a conjecture of F. Bergeron (2020) on the multiplicity of the sign character of $R_n^{(2,1)}$. Finally, using a result of Hogancamp (2017), we enhance a recent result of Gorsky--Mellit (2026) which relates the Khovanov--Rozansky homology of the $(n,n+1)$-torus knot to $R_n^{(2,0)} \\otimes R_n^{(0,1)}$, by showing that the associated Poincaré series for this knot can be computed from the sign component of $R_n^{(2,1)}$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.23297",
  "author_total": 3,
  "authors": [
    {
      "name": "Nicolle González"
    },
    {
      "name": "John Lentfer"
    },
    {
      "name": "Hanna Mularczyk"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dnv5fvj2ztc6r.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.23297",
  "fulltext_url": null,
  "id": "dnv5fvj2ztc6r",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.23297",
  "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"
    ],
    [
      "arxiv",
      "math.GT"
    ],
    [
      "arxiv",
      "math.RT"
    ],
    [
      "openalex",
      "2607|Advanced Combinatorial Mathematics"
    ]
  ],
  "openalex": "W7214053166",
  "pdf_url": "https://arxiv.org/pdf/2609.23297",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dnv5fvj2ztc6r.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.23297",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.23297"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.GT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Sign components of diagonal superspace coinvariants",
  "title_text": "Sign components of diagonal superspace coinvariants",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/dnv5fvj2ztc6r",
  "venue": "arXiv",
  "versions": []
}