{
  "abstract": "We prove that every idempotent Schur multiplier is a finite signed sum of contractive idempotent Schur multipliers. This was conjectured by Katavolos and Paulsen in 2003 and previously known only for translation-invariant Schur multipliers, by the Cohen-Host idempotent theorem. Concretely, we show that any boolean matrix $A$ with Schur multiplier norm at most $γ$ (or equivalently $\\lVert A\\rVert_{γ_2} \\le γ$) can be written as \\[ A=\\sum_{i=1}^{L}σ_i B_i,\\] where $L\\leq 2^{Cγ^6}$ for an absolute constant $C$, $σ_i\\in\\{-1,1\\}$ are signs, and each $B_i$ is a contractive idempotent Schur multiplier, that is, a boolean matrix whose $1$-entries form a union of all-one rectangular blocks, with no two blocks sharing a row or a column. As observed by Carenini, a key lemma in our work yields a new proof of the Cohen-Host theorem and gives a simple proof of the quantitative refinements of Green-Sanders and Sanders, with improved bounds. We include a self-contained exposition of these results in the case of finite groups.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.14316",
  "author_total": 5,
  "authors": [
    {
      "name": "Csongor Beke"
    },
    {
      "name": "Marcel K. Goh"
    },
    {
      "name": "Hamed Hatami"
    },
    {
      "name": "Sean Jaffe"
    },
    {
      "name": "Daniel Naylor"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dv722vbeh594g.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.14316",
  "fulltext_url": null,
  "id": "dv722vbeh594g",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.14316",
  "language": null,
  "licence": "CC-BY-NC-SA-4.0",
  "licence_label": "CC BY-NC-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.CC"
    ],
    [
      "arxiv",
      "math.CA"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "2610|Advanced Operator Algebra Research"
    ]
  ],
  "openalex": "W7169494269",
  "pdf_url": "https://arxiv.org/pdf/2607.14316",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dv722vbeh594g.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:43Z",
      "native_id": "2607.14316",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.14316"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "A characterization of idempotent Schur multipliers",
  "title_text": "A characterization of idempotent Schur multipliers",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:43Z",
  "url": "https://research.draconitic.com/paper/dv722vbeh594g",
  "venue": "arXiv",
  "versions": []
}