Classifying pseudo-ovals, translation generalized quadrangles, and elation Laguerre planes of small order

Giusy Monzillo; Tim Penttila; Alessandro Siciliano

Classifying pseudo-ovals, translation generalized quadrangles, and elation Laguerre planes of small order

Combinatorics 2024-03-01 v1

Authors: Giusy Monzillo , Tim Penttila , Alessandro Siciliano

Abstract

We provide classification results for translation generalized quadrangles of order less or equal to $64$ , and hence, for all incidence geometries related to them. The results consist of the classification of all pseudo-ovals in $PG(3n-1,2)$ , for $n=3,4$ , and that of the pseudo-ovals in $PG(3n-1,q)$ , for $n=5,6$ , such that one of the associated projective planes is Desarguesian.

Keywords

pseudo-ovals translation generalized quadrangles elation Laguerre planes incidence geometries projective planes Desarguesian planes classification

Cite

@article{arxiv.2402.19211,
  title  = {Classifying pseudo-ovals, translation generalized quadrangles, and elation Laguerre planes of small order},
  author = {Giusy Monzillo and Tim Penttila and Alessandro Siciliano},
  journal= {arXiv preprint arXiv:2402.19211},
  year   = {2024}
}

Classifying pseudo-ovals, translation generalized quadrangles, and elation Laguerre planes of small order

Abstract

Keywords

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