{
  "abstract": "Let $H=(V,E)$ be a $k$-uniform hypergraph with polynomial $f_H(\\bm{x})=\\sum_{e\\in E}\\prod_{v\\in e}x_v$. For a finite abelian group $G$ and a subgroup $S$ of $G$, the $k$-partite Cayley hypergraph $K$ has $k$ disjoint vertex parts, each indexed by $G$, and $\\{(1,g_1),\\ldots,(k,g_k)\\}$ is an edge if and only if $g_1+\\cdots+g_k\\in S$. For $k=2$, $K$ is isomorphic to the Bi-Cayley graph associated with $G$ and $S$. For $k\\ge3$, we use character theory to express $f_K$, under a complex unitary change of variables, as a sum of exactly $[G:S]$ nonzero monomials in pairwise disjoint sets of variables. This yields a direct sum decomposition whenever $S$ is a proper subgroup of $G$. When $G=\\Z_2^m$, this transformation is real and orthogonal, enabling us to determine the complete sets of complex E-eigenvalues and Z-eigenvalues of the adjacency tensor of $K$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.28177",
  "author_total": 3,
  "authors": [
    {
      "name": "Yan-Hong Bao"
    },
    {
      "name": "Yi-Zheng Fan"
    },
    {
      "name": "Lili Liao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8qm6f91jv7p9t.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.28177",
  "fulltext_url": null,
  "id": "8qm6f91jv7p9t",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.28177",
  "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.AG"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "arxiv",
      "math.SP"
    ],
    [
      "openalex",
      "2608|Graph theory and applications"
    ]
  ],
  "openalex": "W7223096259",
  "pdf_url": "https://arxiv.org/pdf/2610.28177",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8qm6f91jv7p9t.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:08Z",
      "native_id": "2610.28177",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.28177"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.SP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Fourier Decomposition and E-Eigenvalues of Hypergraph Polynomials over Finite Abelian Groups",
  "title_text": "Fourier Decomposition and E-Eigenvalues of Hypergraph Polynomials over Finite Abelian Groups",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:08Z",
  "url": "https://research.draconitic.com/paper/8qm6f91jv7p9t",
  "venue": "arXiv",
  "versions": []
}