{
  "abstract": "We introduce and study \\emph{constant-sum gap partitions}: for a fixed nonnegative integer $C$, these are partitions $λ=(λ_1,\\ldots,λ_k)$ whose successive differences $d_i=λ_{i+1}-λ_i$ satisfy $d_i+d_{k-i}=C$ for all valid $i$. We derive the generating function for this family, treating partitions of odd and even length separately, and compute it explicitly for $C=0, 1,2,3,4$. We then construct explicit bijections between constant-sum gap partitions with $2m+1$, respectively $2m$, parts and partitions into odd, respectively even, parts in which parts below the largest part have bounded multiplicity, together with an exact weight relation between a partition and its image. Finally, we give a geometric characterization of constant-sum gap partitions in terms of their Ferrers diagrams: removing a prescribed, linearly growing number of cells from each row renders the diagram symmetric about its middle row, for both the odd- and even-length cases.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.06417",
  "author_total": 1,
  "authors": [
    {
      "name": "Halime Ömrüuzun Seyrek"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/881yce4w7ct8c.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.06417",
  "fulltext_url": null,
  "id": "881yce4w7ct8c",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.06417",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.06417",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/881yce4w7ct8c.ris",
  "sources": [
    {
      "first_seen": "2026-11-05T15:21:00Z",
      "native_id": "2611.06417",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.06417"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "On Partitions with Constant-Sum Gap Sequences",
  "title_text": "On Partitions with Constant-Sum Gap Sequences",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:30Z",
  "url": "https://research.draconitic.com/paper/881yce4w7ct8c",
  "venue": "arXiv",
  "versions": []
}