{
  "abstract": "We study a symmetry problem for the $h$-polynomials of edge rings of bipartite graphs. Let $G$ be a bipartite graph and write $h(\\mathbb{k}[G];t)=h_0+h_1t+\\cdots+h_st^s$. We prove that if $\\Bbbk[G]$ is pseudo-Gorenstein and $h_1=h_{s-1}$, then $\\Bbbk[G]$ is Gorenstein. Equivalently, under these assumptions the $h$-polynomial of $\\Bbbk[G]$ is palindromic. The proof treats the $2$-connected case first by translating the numerical condition $h_1=h_{s-1}$ into a tight-separation condition for non-edges, and then passes to arbitrary bipartite graphs using the block decomposition. We also construct a blockwise minimal Gorenstein closure, obtained by adjoining all non-edges not separated by tight acceptable sets, and show that this construction preserves the next-to-leading coefficient of the $h$-polynomial.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.26865",
  "author_total": 1,
  "authors": [
    {
      "name": "Yuta Hatasa"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7y7fdkdq692j8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.26865",
  "fulltext_url": null,
  "id": "7y7fdkdq692j8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.26865",
  "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.AC"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "2602|Commutative Algebra and Its Applications"
    ]
  ],
  "openalex": "W7162512689",
  "pdf_url": "https://arxiv.org/pdf/2605.26865",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7y7fdkdq692j8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:50Z",
      "native_id": "2605.26865",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.26865"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "A palindromicity criterion for the $h$-polynomials of bipartite edge rings",
  "title_text": "A palindromicity criterion for the h-polynomials of bipartite edge rings",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:50Z",
  "url": "https://research.draconitic.com/paper/7y7fdkdq692j8",
  "venue": "arXiv",
  "versions": []
}