{
  "abstract": "By a simple homogenization process, one may turn a $q$-analog into a symmetric $(q,t)$-analog. Although simple, this bijective correspondence makes many concepts and identities become more natural, and proofs follow readily from classical properties of symmetric functions in two variables. A more intricate non-homogeneous extension is also developed. We illustrate this approach, revisiting recent developments in the study of $γ$-positivity, Lucas analogues, and the monoid of Cyclotomic generating functions. This also leads naturally to new constructions and conjectures. We further explore other avenues of investigations, included graded and equivariant $γ$-positivity and $γ$-anti-positivity (also known as alternatingly $γ$-positive).",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.30979",
  "author_total": 1,
  "authors": [
    {
      "name": "François Bergeron"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/aznxtb9gvqps3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.30979",
  "fulltext_url": null,
  "id": "aznxtb9gvqps3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.30979",
  "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": "W7204941737",
  "pdf_url": "https://arxiv.org/pdf/2608.30979",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-31",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/aznxtb9gvqps3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:48Z",
      "native_id": "2608.30979",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.30979"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "A $(q,t)$-Overview of $q$-Analogs",
  "title_text": "A (q,t)-Overview of q-Analogs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:48Z",
  "url": "https://research.draconitic.com/paper/aznxtb9gvqps3",
  "venue": "arXiv",
  "versions": []
}