{
  "abstract": "In this work, we prove that any Boolean function of degree $d$ on $\\mathbb{Z}_{q}^n$, $q\\geq 3$, has at most $m_qq^d$ relevant variables, where $m_q=\\frac{2q(q^2+4q+1)}{(q-1)^4}$. For $q\\in \\{3,4,5,6,7\\}$, we improve this bound to $2.854\\cdot 3^d$, $1.749\\cdot 4^d$, $1.263\\cdot 5^d$, $0.994\\cdot 6^d$, and $0.814\\cdot 7^d$, respectively.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.12540",
  "author_total": 1,
  "authors": [
    {
      "name": "Alexandr Valyuzhenich"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2hax3maz48yrr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.12540",
  "fulltext_url": null,
  "id": "2hax3maz48yrr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.12540",
  "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",
      "1702|Coding theory and cryptography"
    ]
  ],
  "openalex": "W7212864242",
  "pdf_url": "https://arxiv.org/pdf/2609.12540",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2hax3maz48yrr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:11Z",
      "native_id": "2609.12540",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.12540"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "An upper bound on the number of relevant variables in a bounded degree Boolean function on the Hamming graph",
  "title_text": "An upper bound on the number of relevant variables in a bounded degree Boolean function on the Hamming graph",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:11Z",
  "url": "https://research.draconitic.com/paper/2hax3maz48yrr",
  "venue": "arXiv",
  "versions": []
}