{
  "abstract": "In an asymmetric shelf shuffle, a deck of $n$ cards is dealt sequentially from the bottom and assigned one of the $m$ shelves uniformly at random. The card is placed at the top of the assigned shelf with probability $p$, and at the bottom of the assigned shelf with probability $(1-p)$. Analysis of the shelf shuffle has gained much attention recently, and the case $p=1/2$ was first treated by Diaconis--Fulman--Holmes [Ann. Appl. Prob. 23 (2013), no. 4, 1692--1720]. In this paper, we extend the analysis of the shelf shuffle to general $p\\in (0, 1)$. In particular, we study the distribution of cycles, cycle lengths, number of descents, number of valleys, number of inversions, and the RSK shape of a permutation obtained from an asymmetric shelf shuffle. Our results extend the analysis of Diaconis--Fulman--Holmes to arbitrary $p$. Furthermore, our analysis of the distribution of descents and inversions is new even for $p=1/2$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": "Journal reference: Journal of Theoretical Probability 39, 85 (2026)",
  "arxiv": "2606.18047",
  "author_total": 1,
  "authors": [
    {
      "name": "Raghavendra Tripathi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/c5qqwy356evaf.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.18047",
  "fulltext_url": null,
  "id": "c5qqwy356evaf",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.18047",
  "language": null,
  "licence": "CC0-1.0",
  "licence_label": "CC0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/publicdomain/zero/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "arxiv",
      "math.PR"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2606.18047",
  "pmcid": null,
  "pmid": null,
  "published": "2026-06-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/c5qqwy356evaf.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:15Z",
      "native_id": "2606.18047",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.18047"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Analysis of the asymmetric shelf shuffle",
  "title_text": "Analysis of the asymmetric shelf shuffle",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:15Z",
  "url": "https://research.draconitic.com/paper/c5qqwy356evaf",
  "venue": "arXiv",
  "versions": [
    {
      "doi": "10.1007/s10959-026-01547-9",
      "pid": null,
      "relation": "published-as",
      "title": null,
      "venue": null
    }
  ]
}