{
  "abstract": "An addition chain of length $h$ that leads to a number $n$ is a sequence of positive integers $s_0=1,s_1=2,\\ldots,s_h=n$ such that $s_i=s_j+s_k$~($i>j\\geq k$) for each $1\\leq i\\leq h$. We introduce a matrix-theoretic framework for studying the properties of arbitrary addition chains that lead to a target integer $n\\geq 2$ by associating each chain and the sequence of dominant and lower weight summands that calculate each term in the chain an adjacency matrix that encodes the internal geometry. In this linear-algebraic and matrix theoretic framework, we investigate how rank, rank profiles, singular values, eigenvalues, matrix norms, predecessor depths, and track-interaction terms encode the combinatorial and arithmetic structure of addition chains",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "name": "Theophilus Agama"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2h6z68cvzqmb1.bib",
  "cited_by": 0,
  "doi": null,
  "fulltext_url": null,
  "id": "2h6z68cvzqmb1",
  "issns": [],
  "landing_url": "https://hal.science/hal-05763442v1",
  "language": "en",
  "licence": "CC-BY-ND-4.0",
  "licence_label": "CC BY-ND 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by-nd/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "hal",
      "0.math"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://hal.science/hal-05763442/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2h6z68cvzqmb1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:40Z",
      "native_id": "hal-05763442",
      "source": "hal",
      "url": "https://hal.science/hal-05763442v1"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "hal:0.math",
      "subfield": "general"
    }
  ],
  "title": "MATRIX THEORETIC AND COMBINATORIAL STRUCTURES IN ADDITION CHAINS",
  "title_text": "MATRIX THEORETIC AND COMBINATORIAL STRUCTURES IN ADDITION CHAINS",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:40Z",
  "url": "https://research.draconitic.com/paper/2h6z68cvzqmb1",
  "venue": "HAL",
  "versions": []
}