Skip to content
DraconiticResearch
Search Sources API
203,234 studies31 sourcesUpdated 30 min ago
Peer-reviewedCC BY 4.0Axioms

Point-Cyclic Resolutions of 2-(64, 4, 1) Designs

  • Svetlana Topalova1,2
  • Stela Zhelezova1
  1. 1Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, 1113 Sofia, Bulgaria
  2. 2Centre of Excellence in Informatics and Information and Communication Technologies, 1113 Sofia, Bulgaria
Open at sourceDOICite

Abstract

A point-cyclic resolution of a 2-(v,k,1) design is invariant under a cyclic automorphism group of order v. Point-cyclic resolutions are of interest for their relations to many other combinatorial structures, and for their various applications. Resolutions of 2-(v,4,1) designs can exist if v≡4(mod 12). There are six point-cyclic resolutions of 2-(v,4,1) designs with v<64. Before the present study, v=64 was the smallest v for which neither theoretical nor constructive results on the existence of point-cyclic resolutions of 2-(v,4,1) designs were known. We establish that there are 258 point-cyclic resolutions of 2-(64,4,1) designs. The investigation is computer-aided.

Related

  1. Resolutions of linear p-cyclic quotient singularities
    Linghu Fan, Hongmin Li
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  2. Quasi-uniform designs from random candidates: optimal candidate complexity and farthest-point sampling
    Takashi Goda, Hengjun Xu
    arXivPreprintCC BY-NC-ND 4.0Full textNumerical analysis & scientific computingarXiv
  3. Characterizing multigraded regularity and virtual resolutions on products of projective spaces
    Juliette Bruce, Lauren Cranton Heller, Mahrud Sayrafi
    Advances in MathematicsPeer-reviewedLicence not statedFull text20 citedAlgebra & number theoryOpenAlex
  4. Isolated symplectic singularities admitting symplectic resolutions
    Duo Li, Yanjie Li
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  5. Flasque resolutions and almost strong approximation
    Jean-Louis Colliot-Thélène
    HALPreprintCC BY-NC-ND 4.0Full textAlgebra & number theoryHAL

Cite

BibTeXRIS
BibTeX
@article{topalova2026pointcyclic,
  title = {{Point-Cyclic Resolutions of 2-(64, 4, 1) Designs}},
  author = {Svetlana Topalova and Stela Zhelezova},
  journal = {Axioms},
  year = {2026},
  month = oct,
  doi = {10.3390/axioms15100762},
  url = {https://www.mdpi.com/2075-1680/15/10/762},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Point-Cyclic Resolutions of 2-(64, 4, 1) Designs
AU  - Svetlana Topalova
AU  - Stela Zhelezova
PY  - 2026
DA  - 2026/10/13
JO  - Axioms
DO  - 10.3390/axioms15100762
UR  - https://www.mdpi.com/2075-1680/15/10/762
AB  - A point-cyclic resolution of a 2-(v,k,1) design is invariant under a cyclic automorphism group of order v. Point-cyclic resolutions are of interest for their relations to many other combinatorial structures, and for their various applications. Resolutions of 2-(v,4,1) designs can exist if v≡4(mod 12). There are six point-cyclic resolutions of 2-(v,4,1) designs with v<64. Before the present study, v=64 was the smallest v for which neither theoretical nor constructive results on the existence of point-cyclic resolutions of 2-(v,4,1) designs were known. We establish that there are 258 point-cyclic resolutions of 2-(64,4,1) designs. The investigation is computer-aided.
SN  - 2075-1680
ER  -