Cameron-Liebler sets of generators in the Klein quadric Q⁺(5,q)

2025/03/11 by D'haeseleer, Jozefien, Mannaert, Jonathan, Storme, Leo
#05B25 #51A50 #51E20 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2503.08260

Abstract

We investigate Cameron-Liebler sets of planes in the Klein quadric Q⁺(5,q) in PG(5,q). We prove that there are many examples of such Cameron-Liebler sets of planes in the Klein quadric. More specifically, we provide an incomplete list of examples of such Cameron-Liebler sets of planes. By doing so, we also provide some characteristic results regarding these sets in connection with the Klein quadric. These results contribute to an open conjecture posed in [21].

Related

• On two non-existence results for Cameron-Liebler k-sets in PG(n,q)
• Cameron-Liebler sets of k-spaces in PG(n,q)
• Cameron-Liebler line classes with parameter x=(q²-1)/(2)
• A note on Cameron - Liebler line classes in PG(n,4)
• Cameron-Liebler sets in bilinear forms graphs