A common generalization of hypercube partitions and ovoids in polar spaces

D’haeseleer, Jozefien; Ihringer, Ferdinand; Schmidt, Kai-Uwe

doi:10.1007/s10623-024-01489-5

Des. Codes Cryptogr.

2024

DOI: 10.1007/s10623-024-01489-5

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A common generalization of hypercube partitions and ovoids in polar spaces

Jozefien D’haeseleer,

Ferdinand Ihringer,

Kai-Uwe Schmidt

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Tactical decompositions in finite polar spaces and non-spreading classical group actions

Bamberg,

Giudici,

Lansdown

et al. 2024

Des. Codes Cryptogr.

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For finite classical groups acting naturally on the set of points of their ambient polar spaces, the symmetry properties of synchronising and separating are equivalent to natural and well-studied problems on the existence of certain configurations in finite geometry. The more general class of spreading permutation groups is harder to describe, and it is the purpose of this paper to explore this property for finite classical groups. In particular, we show that for most finite classical groups, their natural action on the points of its polar space is non-spreading. We develop and use a result on tactical decompositions (an AB-Lemma) that provides a useful technique for finding witnesses for non-spreading permutation groups. We also consider some of the other primitive actions of the classical groups.

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Tactical decompositions in finite polar spaces and non-spreading classical group actions

Bamberg,

Giudici,

Lansdown

et al. 2024

Des. Codes Cryptogr.

View full text Add to dashboard Cite

show abstract

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A common generalization of hypercube partitions and ovoids in polar spaces

Cited by 1 publication

References 13 publications

Tactical decompositions in finite polar spaces and non-spreading classical group actions

Tactical decompositions in finite polar spaces and non-spreading classical group actions

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