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Linear sets from projection of Desarguesian spreads
- Publication Year :
- 2020
-
Abstract
- Every linear set in a Galois space is the projection of a subgeometry, and most known characterizations of linear sets are given under this point of view. For instance, scattered linear sets of pseudoregulus type are obtained by considering a Desarguesian spread of a subgeometry and projecting from a vertex which is spanned by all but two director spaces. In this paper we introduce the concept of linear sets of $h$-pseudoregulus type, which turns out to be projected from the span of an arbitrary number of director spaces of a Desarguesian spread of a subgeometry. Among these linear sets, we characterize those which are $h$-scattered and solve the equivalence problem between them; a key role is played by an algebraic tool recently introduced in the literature and known as Moore exponent set. As a byproduct, we classify asymptotically $h$-scattered linear sets of $h$-pseudoregulus type.
- Subjects :
- Mathematics - Combinatorics
05B25, 51E20, 51E22
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2001.08685
- Document Type :
- Working Paper