{
  "abstract": "Let $G$ and $H$ be Gram matrices of spherical $2$-designs on the same number of indices. We study when their Schur product is again the Gram matrix of a spherical design. We give a criterion in terms of orthogonal projections with constant diagonal, and an explicit $15$-point spherical $3$-design whose Gram matrix belongs to no symmetric Bose-Mesner algebra. For a symmetric association scheme, the factorization problem takes the form $v(E_S\\circ E_T)=μE_U$. This is a counterpart of ordinary matrix product factorizations in the adjacency basis. The case $E_U=I-E_0$ gives a dual near-factorization and has a regular simplex as its normalized output. We characterize complementary input supports by a strongly regular fusion, give a reciprocal criterion, and classify the case in which one factor is the last Hamming idempotent.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.34598",
  "author_total": 2,
  "authors": [
    {
      "name": "Bobby Miraftab"
    },
    {
      "name": "Sho Suda"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ede6jjmeaz984.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.34598",
  "fulltext_url": null,
  "id": "ede6jjmeaz984",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.34598",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "2607|Finite Group Theory Research"
    ]
  ],
  "openalex": "W7224018363",
  "pdf_url": "https://arxiv.org/pdf/2610.34598",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ede6jjmeaz984.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.34598",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.34598"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Dual near-factorizations and Schur products in association schemes",
  "title_text": "Dual near-factorizations and Schur products in association schemes",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/ede6jjmeaz984",
  "venue": "arXiv",
  "versions": []
}