{
  "abstract": "The reflection complexity of a sequence, introduced recently by Allouche, Campbell, Li, Shallit, and Stipulanti, counts the factors of a given length up to reversal. We generalize this notion considering a group $G$ generated by antimorphisms over a given alphabet $\\mathcal A$. The $G$-complexity of a sequence over $\\mathcal A$ counts the factors of a given length up to the action of $G$. For $G$ generated by the reflection alone, the $G$-complexity coincides with the reflection complexity. We characterize eventual periodicity in terms of the $G$-complexity. Then we focus on the binary alphabet and the group $H$ generated by reflection and the antimorphism exchanging letters. We provide a simple formula for the $H$-complexity in the case of $H$-rich sequences and determine the precise values for complementary symmetric Rote sequences and generalized binary Thue-Morse sequences. Finally, we describe the aperiodic recurrent sequences having the minimum $H$-complexity -- they are exactly the complementary symmetric Rote sequences, while the binary sequences with the minimum reflection complexity correspond to the Sturmian sequences.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.14637",
  "author_total": 3,
  "authors": [
    {
      "name": "Adam Blažek"
    },
    {
      "name": "Lubomíra Dvořáková"
    },
    {
      "name": "Edita Pelantová"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/18kege6czerw6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.14637",
  "fulltext_url": null,
  "id": "18kege6czerw6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.14637",
  "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.CO"
    ],
    [
      "openalex",
      "1703|semigroups and automata theory"
    ]
  ],
  "openalex": "W7221787930",
  "pdf_url": "https://arxiv.org/pdf/2610.14637",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/18kege6czerw6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.14637",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.14637"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Generalized reflection complexity",
  "title_text": "Generalized reflection complexity",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/18kege6czerw6",
  "venue": "arXiv",
  "versions": []
}