{
  "abstract": "A generalization of fixed-lattice cluster expansions (CE) and atomic cluster expansions (ACE) is presented that expresses both rotation and permutation symmetries. By performing Schur--Weyl decomposition in Young subgroup-stabilized carriers, followed by joint coupling of rotation and permutation representations, arbitrary $S_N\\times SO(3)$ tensor product carriers are generated. This allows us to resolve complete, orthonormal joint rotation and permutation-adapted bases for arbitrary tensor product ranks and arbitrary angular and radial tensor product content. We show that this very general Young--E(3) (YE3T) tensor product basis contains the ACE basis as a subset, corresponding to the special case where permutation symmetry character is restricted to the fully symmetric carrier. Rather than constructing an overcomplete rotation and permutation-invariant basis and reducing it \\textit{a posteriori}, Barthelemy \\textit{et al.} recently demonstrated scaling benefits by not constructing an overcomplete basis. YE3T directly produces a complete orthonormal basis without an overcomplete step and rigorously extends to permutation characters beyond permutation-symmetric features. The YE3T decomposition yields new joint irreducible rotation- and permutation-equivariant basis sets that surpass existing rotation-adapted expansions in both speed and accuracy, defining a new Pareto front for machine-learned interatomic potentials. We show that the tunability of the permutation symmetry character makes the basis useful for both atomistic and electronic-structure simulations.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.31895",
  "author_total": 2,
  "authors": [
    {
      "name": "James M. Goff"
    },
    {
      "name": "Aidan P. Thompson"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/19erymc9gmn2b.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.31895",
  "fulltext_url": null,
  "id": "19erymc9gmn2b",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.31895",
  "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",
      "cond-mat.mtrl-sci"
    ],
    [
      "openalex",
      "2505|Machine Learning in Materials Science"
    ]
  ],
  "openalex": "W7214755545",
  "pdf_url": "https://arxiv.org/pdf/2609.31895",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/19erymc9gmn2b.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:12Z",
      "native_id": "2609.31895",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.31895"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.mtrl-sci",
      "subfield": "condensed-matter"
    }
  ],
  "title": "The Young-E(3) Tensor Product Decomposition for Rotation and Permutation Equivariant Cluster Expansions",
  "title_text": "The Young-E(3) Tensor Product Decomposition for Rotation and Permutation Equivariant Cluster Expansions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:12Z",
  "url": "https://research.draconitic.com/paper/19erymc9gmn2b",
  "venue": "arXiv",
  "versions": []
}