{
  "abstract": "We consider pairs of maps $(f,g)$, where $f$ is an $n$-valued map and $g$ is an $m$-valued map, defined on connected finite polyhedra. A point $x$ such that $f(x)\\cap g(x)\\neq \\emptyset$ is called a coincidence point of $f$ and $g$. A useful device for studying coincidence points would be a Nielsen-type invariant which provides a lower bound for the number of coincidence points of all $(n, m)$-valued pairs of maps homotopic to $(f,g)$. The construction of such an invariant $N(f:g)$ was proposed in [J. Fixed Point Theory Appl. 14, 309--324 (2013)]. Unfortunately, this approach has some flaws. In this paper, we present a modified construction that yields a corrected form of the invariant, defined in terms of the intersection points of the graphs of $f$ and $g$. In the case of $(n, m)$-valued pairs of maps of the circle our invariant provides a sharp lower bound, which we precisely determine.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": "Journal reference: J. Fixed Point Theory Appl. 28, 91 (2026)",
  "arxiv": "2605.07015",
  "author_total": 3,
  "authors": [
    {
      "name": "Grzegorz Graff"
    },
    {
      "name": "P. Christopher Staecker"
    },
    {
      "name": "Alan Żeromski"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/akthr7wcm1zq5.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.07015",
  "fulltext_url": null,
  "id": "akthr7wcm1zq5",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.07015",
  "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.GN"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2605.07015",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/akthr7wcm1zq5.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2605.07015",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.07015"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GN",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Nielsen coincidence theory of $(n,m)$-valued pairs of maps",
  "title_text": "Nielsen coincidence theory of (n,m)-valued pairs of maps",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/akthr7wcm1zq5",
  "venue": "arXiv",
  "versions": [
    {
      "doi": "10.1007/s11784-026-01344-1",
      "pid": null,
      "relation": "published-as",
      "title": null,
      "venue": null
    }
  ]
}