{
  "abstract": "Given a permutation $τ$ on $n$ letters, we consider lattices spanned by an orbit of one vector $\\boldsymbol x$ in $\\mathbb R^n$ under the action of $τ$ by permutation of the coordinates. Such lattices generalize the important class of cyclic lattices and have previously been studied in~\\cite{perm}, where a bound on their rank was established. We prove a sufficient condition on $\\boldsymbol x$ for this bound to be achieved. We further investigate the structure of such permutation-invariant lattices, proving that they are glued by the permuted vector from the orthogonal cyclic blocks and giving a determinant formula for the lattice in terms of determinants of these blocks and the norm of the permuted vector. In the case $\\boldsymbol x$ is an integer vector, these blocks are sublattices of the root lattices $A_k$ in respective dimensions with root lattices themselves and their glued direct sums also realizable by this construction. We also exhibit a glued construction of permutation-invariant algebraic integral lattices from collections of cyclic number fields. Finally, we prove a strengthened version of a previous result of~\\cite{lf_ek} on a related construction of well-rounded lattices spanned by sets of algebraic conjugates.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.20952",
  "author_total": 2,
  "authors": [
    {
      "name": "Maria Fernanda Zordan Bonini"
    },
    {
      "name": "Lenny Fukshansky"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0a53yjwwxgaw8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.20952",
  "fulltext_url": null,
  "id": "0a53yjwwxgaw8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.20952",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2610|Advanced Algebra and Geometry"
    ]
  ],
  "openalex": "W7213887587",
  "pdf_url": "https://arxiv.org/pdf/2609.20952",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0a53yjwwxgaw8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:07Z",
      "native_id": "2609.20952",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.20952"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "On permutation-invariant construction of glued lattices",
  "title_text": "On permutation-invariant construction of glued lattices",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:07Z",
  "url": "https://research.draconitic.com/paper/0a53yjwwxgaw8",
  "venue": "arXiv",
  "versions": []
}