Partial k-Parallelisms in Finite Projective Spaces

Tuvi Etzion

Partial k-Parallelisms in Finite Projective Spaces

Combinatorics 2013-12-20 v2

Authors: Tuvi Etzion

Abstract

In this paper we consider the following question. What is the maximum number of pairwise disjoint $k$ -spreads which exist in PG(n,q)? We prove that if k+1 divides n+1 and n>k then there exist at least two disjoint k-spreads in PG(n,q) and there exist at least $2^{k+1}-1$ pairwise disjoint $k$ -spreads in PG(n,2). We also extend the known results on parallelism in a projective geometry from which the points of a given subspace were removed.

Keywords

linear sets incidence geometry of points and lines projective geometry

Cite

@article{arxiv.1302.3629,
  title  = {Partial k-Parallelisms in Finite Projective Spaces},
  author = {Tuvi Etzion},
  journal= {arXiv preprint arXiv:1302.3629},
  year   = {2013}
}

Comments

arXiv admin note: text overlap with arXiv:0805.3528 by other authors

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