{
  "abstract": "Let $$ S=\\mathbb{C}[x,y,z],\\qquad p_m=x^m+y^m+z^m. $$ For every $r\\geq1$, we prove that $$ p_r,\\ p_{r+1},\\ p_{3r+1} \\qquad\\text{and}\\qquad p_r,\\ p_{r+1},\\ p_{3r+2} $$ are regular sequences exactly when $r\\not\\equiv1\\pmod3$. This proves the Conca--Krattenthaler--Watanabe prediction for two infinite families. The proof is elementary. Four simple reductions modulo $(p_r,p_{r+1})$ reduce the problem to the two equations $x+y+z=0$ and $xy+xz+yz=0$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.07932",
  "author_total": 1,
  "authors": [
    {
      "name": "Abed Abedelfatah"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0hkv86a1wfg00.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.07932",
  "fulltext_url": null,
  "id": "0hkv86a1wfg00",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.07932",
  "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.AC"
    ],
    [
      "openalex",
      "2602|Commutative Algebra and Its Applications"
    ]
  ],
  "openalex": "W7212072854",
  "pdf_url": "https://arxiv.org/pdf/2609.07932",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0hkv86a1wfg00.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.07932",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.07932"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Two Infinite Families of Regular Sequences of Power Sums in Three Variables",
  "title_text": "Two Infinite Families of Regular Sequences of Power Sums in Three Variables",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/0hkv86a1wfg00",
  "venue": "arXiv",
  "versions": []
}