{
  "abstract": "For a bipartite graph $G$ and an integer $t\\geq2$, let $\\NM_t(G)$ be its $t$-non-matching complex. We prove that adding an edge while preserving bipartiteness induces an injection on reduced homology in degree $2t-3$. Combined with the cyclic-polytope model for non-matching complexes of cycles, this shows that $\\NM_t(G)$ has Leray number $2t-2$ whenever $G$ contains a cycle of length at least $2t$. Under the same hypothesis, Hochster's formula yields regularity $2t-1$ for the Stanley-Reisner ideal $I_{\\NM_t(G)}$, together with explicit lower bounds for the Betti numbers on its top regularity strand and for its projective dimension. If $G$ contains a $2t$-cycle, we also determine the maximal shifts of $I_{\\NM_t(G)}$ through homological degree $|E(G)|-2t+1$. For $G=K_{r,s}$ with $2\\leq t\\leq r\\leq s$, we determine the depth, projective dimension, all maximal shifts, and the unique extremal Betti number of $I_{\\NM_t(K_{r,s})}$, thereby settling a conjecture on facet ideals of chessboard complexes.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.02621",
  "author_total": 2,
  "authors": [
    {
      "name": "Jiawen Shan"
    },
    {
      "name": "Zexin Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1sxjfbcrwty52.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.02621",
  "fulltext_url": null,
  "id": "1sxjfbcrwty52",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.02621",
  "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"
    ],
    [
      "openalex",
      "2602|Commutative Algebra and Its Applications"
    ]
  ],
  "openalex": "W7207521037",
  "pdf_url": "https://arxiv.org/pdf/2609.02621",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1sxjfbcrwty52.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:20Z",
      "native_id": "2609.02621",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.02621"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Homology of non-matching complexes under edge additions and applications to their Stanley-Reisner ideals",
  "title_text": "Homology of non-matching complexes under edge additions and applications to their Stanley-Reisner ideals",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:20Z",
  "url": "https://research.draconitic.com/paper/1sxjfbcrwty52",
  "venue": "arXiv",
  "versions": []
}