{
  "abstract": "Andrews and Newman \\cite{AN19, AN20} defined the minimal excludant or mex of a partition. The mex of a partition is the smallest positive integer which is absent from the partition. Baruah, Bhoria, Eyyunni and Maji \\cite{BBEM} studied the sum of mex split according to parity, together with its $\\ell$-th moments. Ballantine and Merca \\cite{BM20} generalized mex to the least $s$-gap, which is the smallest natural number that does not occur minimum $s$ times in the partition. Baruah and Talukdar \\cite{BT} conjectured a corresponding asymptotic equivalence between the sums of odd and even least $s$-gaps for every $s>1$, generalizing a theorem of Barman and Singh \\cite{BS} for the classical mex. In this article, we derive exact formulas for the $\\ell$-th moments of $\\smex(π)$ for every fixed $\\ell\\ge 1$, in terms of partition functions. We give a complete proof of the conjecture of Baruah and Talukdar \\cite{BT} for every natural number $s>1$. We also generalize an identity of Hopkins, Sellers and Stanton \\cite{HSS} to the least $s$-gap setting.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.31104",
  "author_total": 2,
  "authors": [
    {
      "name": "Sourav Bhowmick"
    },
    {
      "name": "Nabin Kumar Meher"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8ny37zs266e1d.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.31104",
  "fulltext_url": null,
  "id": "8ny37zs266e1d",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.31104",
  "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.CO"
    ],
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2602|Advanced Mathematical Identities"
    ]
  ],
  "openalex": "W7214650062",
  "pdf_url": "https://arxiv.org/pdf/2609.31104",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8ny37zs266e1d.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:28:40Z",
      "native_id": "2609.31104",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.31104"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "On the Moments of Least $s$-Gaps of Partitions and a Conjecture of Baruah and Talukdar",
  "title_text": "On the Moments of Least s-Gaps of Partitions and a Conjecture of Baruah and Talukdar",
  "type": "preprint",
  "updated_at": "2026-10-30T12:28:40Z",
  "url": "https://research.draconitic.com/paper/8ny37zs266e1d",
  "venue": "arXiv",
  "versions": []
}