Skip to content
DraconiticResearch
Search Sources API
201,818 studies31 sourcesUpdated 30 min ago
PreprintCC BY-NC-ND 4.0HAL

Fractal Hyper-Trees: Combinatorial Enumeration, Symmetry Properties, and Ultrametric Structures

  • Jean-Jacques Salone
Open at sourcePDFDOICite

Abstract

This paper introduces and formalizes Fractal Hyper-Trees (FHT), a novel class of hypergraphs characterized by deep recursive inclusion hierarchies and controlled relational textures. Moving beyond classical graph-theoretic frameworks, we establish an axiomatic foundation for FHTs and investigate their combinatorial enumeration, revealing explicit connections to OEIS sequence A398931. Furthermore, we analyze the structural symmetry properties via automorphism groups, examine the resulting global hierarchical ultrametric topologies, and discuss asymptotic perspectives, including vertex substitution operators and heuristic parallels with p-adic integer rings.

Related

  1. From wall structures to closed mirror symmetry. The case of Kℙ2: Renormalized periods over the positive real locus, closed Gromov-Witten invariants from wall functions, and tropical enumeration
    Michel van Garrel, Bernd Siebert
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv
  2. Baxter Structures and the Odd-Even Enumeration of Red-Blue Motzkin Paths
    Joanna N. Chen
    arXivPreprintarXiv licenceFull textCombinatorics & discrete mathematicsarXiv
  3. Intractable enumeration problems are like Russian nesting dolls: structural properties of monomer-dimer coverings on two-dimensional quadratic lattices
    Yong Kong
    arXivPreprintarXiv licenceFull textCombinatorics & discrete mathematicsStatistical & nonlinear physicsarXiv
  4. Perfect Combinatorial Structures in Coding Theory and Cryptography
    Vladimir N. Potapov
    arXivPreprintarXiv licenceFull textCombinatorics & discrete mathematicsarXiv
  5. MATRIX THEORETIC AND COMBINATORIAL STRUCTURES IN ADDITION CHAINS
    Theophilus Agama
    HALPreprintCC BY-ND 4.0Full textGeneral mathematicsHAL

Cite

BibTeXRIS
BibTeX
@misc{salone2026fractal,
  title = {{Fractal Hyper-Trees: Combinatorial Enumeration, Symmetry Properties, and Ultrametric Structures}},
  author = {Jean-Jacques Salone},
  howpublished = {HAL},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.19895},
  eprint = {2609.19895},
  archivePrefix = {arXiv},
  url = {https://hal.science/hal-05748266v1},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - Fractal Hyper-Trees: Combinatorial Enumeration, Symmetry Properties, and Ultrametric Structures
AU  - Jean-Jacques Salone
PY  - 2026
DA  - 2026/09/13
PB  - HAL
DO  - 10.48550/arxiv.2609.19895
UR  - https://hal.science/hal-05748266v1
AB  - This paper introduces and formalizes Fractal Hyper-Trees (FHT), a novel class of hypergraphs characterized by deep recursive inclusion hierarchies and controlled relational textures. Moving beyond classical graph-theoretic frameworks, we establish an axiomatic foundation for FHTs and investigate their combinatorial enumeration, revealing explicit connections to OEIS sequence A398931. Furthermore, we analyze the structural symmetry properties via automorphism groups, examine the resulting global hierarchical ultrametric topologies, and discuss asymptotic perspectives, including vertex substitution operators and heuristic parallels with p-adic integer rings.
ER  -