{
  "abstract": "The algebra of polysymmetric functions (PSym) is defined as the tensor product of copies of the algebra of symmetric functions (Sym) where the $i$th copy has variables scaled by $i$. One way to construct a basis of PSym is to start with a basis $\\{f_λ\\}$ of Sym and consider all pure tensors arising from this basis. Asvin G and Andrew O'Desky described four families of non-pure tensor bases, namely $H, E, E^+$ and $P$, which we call plethystic bases. In this paper, we study the expansions of the plethystic bases into the pure-tensor bases $\\{h^\\otimes_τ\\}$ and $\\{e^\\otimes_τ\\}$, and interpret the results via combinatorial objects called polywrapping block tabloids. The expansions of $H, E$ and $E^+$ in $h^\\otimes$ and $e^\\otimes$ are found via the $h$-expansion of the plethysm $h_n[p_r]$. We compute this $h$-expansion using a statistic on words and prove it through abacus methods.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.36181",
  "author_total": 1,
  "authors": [
    {
      "name": "Aditya Khanna"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9crw8zdyjn7ca.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.36181",
  "fulltext_url": null,
  "id": "9crw8zdyjn7ca",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.36181",
  "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"
    ],
    [
      "openalex",
      "2607|Advanced Combinatorial Mathematics"
    ]
  ],
  "openalex": "W7214994728",
  "pdf_url": "https://arxiv.org/pdf/2609.36181",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9crw8zdyjn7ca.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:35Z",
      "native_id": "2609.36181",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.36181"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "The $h$-expansion of the Plethysm $h_n[p_r]$ and Polysymmetric Expansions in $h^\\otimes$ and $e^\\otimes$",
  "title_text": "The h-expansion of the Plethysm h_n[p_r] and Polysymmetric Expansions in h^⊗ and e^⊗",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:35Z",
  "url": "https://research.draconitic.com/paper/9crw8zdyjn7ca",
  "venue": "arXiv",
  "versions": []
}