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PreprintarXiv licencearXiv

Erdős-Ko-Rado properties of Steiner 2-designs

  • Sam Adriaensen
  • Sergey Goryainov
  • Elena V. Konstantinova
  • Vedran Krčadinac
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Abstract

In this paper, we prove an Erdős-Ko-Rado characterisation of maximum intersecting families of blocks in Steiner $2$-designs arising from Desarguesian maximal arcs. This answers a recent question of Goryainov and Konstantinova, and implies that, among the known Steiner $2$-designs, only finitely many admit a maximum intersecting family that is neither canonical nor associated with a subdesign. We also perform a computational study of $2−(120,8,1)$ designs and find strong counterexamples to a problem of Godsil and Meagher. Finally, we give a parametric generalisation of $2−(66,6,1)$ designs with tight dual arcs as non-canonical maximum intersecting families.

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Cite

BibTeXRIS
BibTeX
@misc{adriaensen2026erdőskorado,
  title = {{Erdős-Ko-Rado properties of Steiner 2-designs}},
  author = {Sam Adriaensen and Sergey Goryainov and Elena V. Konstantinova and Vedran Krčadinac},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.26607},
  eprint = {2609.26607},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.26607},
}
RIS
TY  - UNPB
TI  - Erdős-Ko-Rado properties of Steiner 2-designs
AU  - Sam Adriaensen
AU  - Sergey Goryainov
AU  - Elena V. Konstantinova
AU  - Vedran Krčadinac
PY  - 2026
DA  - 2026/09/22
PB  - arXiv
DO  - 10.48550/arxiv.2609.26607
UR  - https://arxiv.org/abs/2609.26607
AB  - In this paper, we prove an Erdős-Ko-Rado characterisation of maximum intersecting families of blocks in Steiner $2$-designs arising from Desarguesian maximal arcs. This answers a recent question of Goryainov and Konstantinova, and implies that, among the known Steiner $2$-designs, only finitely many admit a maximum intersecting family that is neither canonical nor associated with a subdesign. We also perform a computational study of $2−(120,8,1)$ designs and find strong counterexamples to a problem of Godsil and Meagher. Finally, we give a parametric generalisation of $2−(66,6,1)$ designs with tight dual arcs as non-canonical maximum intersecting families.
ER  -