Skip to content
DraconiticResearch
Search Sources API
190,839 studies31 sourcesUpdated 37 min ago
PreprintCC BY 4.0arXiv

The Higman-Sims graph and a geometric construction of the Steiner system $S(3,6,22)$

  • Mahdi Ebrahimi
Open at sourcePDFDOICite

Abstract

The Higman-Sims graph is the unique strongly regular graph with parameters $(100,22,0,6)$. In this paper, we show that the only distance-regular antipodal double cover of the Higman-Sims graph is its bipartite double cover. Our main tool is a geometric construction of the Steiner system $S(3,6,22)$.

Related

  1. A geometric construction of supercuspidal representations
    Ben Liu, Sian Nie, Zhihang Yu
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  2. How Much Graph Is Too Much? Graph Construction and Exposure in Spatio-Temporal Forecasting
    Saj Maru, Qiyu Han, Krishna Mamidala
    arXivPreprintarXiv licenceFull textStatisticsarXiv
  3. Hyperbolic groups satisfy the Boone–Higman conjecture
    James Belk, Collin Bleak, Francesco Matucci +1
    Duke Mathematical JournalPeer-reviewedLicence not statedFull text5 citedGeometry & topologyOpenAlex
  4. Realizing graph automorphisms as geometric symmetries of straight line drawings
    Saul D. Freedman, Melissa Lee, Dragan Marušič +1
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryCombinatorics & discrete mathematicsarXiv
  5. A Dubnov-Ivanov-Nagata-Higman Theorem for NIP nilrings
    Christian d'Elbée, Yanis Davoust, Jules Tindzogho Ntsiri
    arXivPreprintarXiv licenceFull textLogic & foundationsarXiv

Cite

BibTeXRIS
BibTeX
@misc{ebrahimi2026higmansims,
  title = {{The Higman-Sims graph and a geometric construction of the Steiner system $S(3,6,22)$}},
  author = {Mahdi Ebrahimi},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.07407},
  eprint = {2611.07407},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.07407},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - The Higman-Sims graph and a geometric construction of the Steiner system $S(3,6,22)$
AU  - Mahdi Ebrahimi
PY  - 2026
DA  - 2026/11/05
PB  - arXiv
DO  - 10.48550/arxiv.2611.07407
UR  - https://arxiv.org/abs/2611.07407
AB  - The Higman-Sims graph is the unique strongly regular graph with parameters $(100,22,0,6)$. In this paper, we show that the only distance-regular antipodal double cover of the Higman-Sims graph is its bipartite double cover. Our main tool is a geometric construction of the Steiner system $S(3,6,22)$.
ER  -