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A Characterization of the Natural Embedding of the Split Cayley Hexagon in PG(6,q) by Intersection Numbers in Finite Projective Spaces of Arbitrary Dimension
- Source :
- Discrete Mathematics, 314, 42-49 (2014). ISSN 0012-365X
- Publication Year :
- 2013
-
Abstract
- We prove that a non-empty set L of at most q^5+q^4+q^3+q^2+q+1 lines of PG(n, q) with the properties that (1) every point of PG(n,q) is incident with either 0 or q+1 elements of L, (2) every plane plane of PG(n, q) is incident with either 0, 1 or q+1 elements of L, (3) every solid of PG(n, q) is incident with either 0, 1, q+1 or 2q+1 elements of L, and (4) every 4-dimensional subspace of PG(n, q) is incident with at most q^3-q^2+4q elements of L, is necessarily the set of lines of a split Cayley hexagon H(q) naturally embedded in PG(6, q).
- Subjects :
- Mathematics - Combinatorics
51E12, 51E20
Subjects
Details
- Database :
- arXiv
- Journal :
- Discrete Mathematics, 314, 42-49 (2014). ISSN 0012-365X
- Publication Type :
- Report
- Accession number :
- edsarx.1307.8262
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1016/j.disc.2013.09.012