Cameron-Liebler line classes in \(\mathrm{AG}(3,q)\). (English) Zbl 1459.51002
A set of pairwise disjoint lines is called a partial line spread and a line spread is a partial line spread that partitions the points of the corresponding space. A Cameron-Liebler line class, of parameter \(x\) in both \(\mathrm{PG}(3, q)\) or \(\mathrm{AG}(3, q)\) is a set of lines, such that for every line spread \(S\), we have \(|L \cap S| = x\). The authors generalize the concept of Cameron-Liebler line classes to \(\mathrm{AG}(3,q)\) from \(\mathrm{PG}(3,q)\) and give a link to the Cameron-Liebler line classes in \(\mathrm{PG}(3, q).\) They give some equivalent ways to understand Cameron-Liebler line classes in \(\mathrm{AG}(3,q)\) and some classification results.
Reviewer: Steven T. Dougherty (Scranton)
MSC:
| 51E20 | Combinatorial structures in finite projective spaces |
| 05B25 | Combinatorial aspects of finite geometries |
| 51E14 | Finite partial geometries (general), nets, partial spreads |
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