### Direct constructions of hyperplanes of dual polar spaces arising from embeddings

Bart De Bruyn UGent (2010) 14(2). p.193-209
abstract
Let e be one of the following full projective embeddings of a finite dual polar space Delta of rank n >= 2: (i) The Grassmann-embedding of the symplectic dual polar space Delta congruent to DW(2n 1,q); (ii) the Grassmann-embedding of the Hermitian dual polar space Delta congruent to DH(2n-1, q(2)); (iii) the spin-embedding of the orthogonal dual polar space Delta congruent to DQ(2n, q); (iv) the spin-embedding of the orthogonal dual polar space Delta congruent to DQ(-)(2n+ 1, q). Let H-e denote the set of all hyperplanes of Delta arising from the embedding e. We give a method for constructing the hyperplanes of H-e without implementing the embedding e and discuss (possible) applications of the given construction.
author
organization
year
type
journalArticle (original)
publication status
published
subject
keyword
OVOIDS, FINITE-FIELDS, GENERATION, spin-embedding, Grassmann-embedding, dual polar space, hyperplane
journal title
ANNALS OF COMBINATORICS
Ann. Comb.
volume
14
issue
2
pages
193 - 209
Web of Science type
Article
Web of Science id
000278572900002
JCR category
MATHEMATICS, APPLIED
JCR impact factor
0.462 (2010)
JCR rank
186/235 (2010)
JCR quartile
4 (2010)
ISSN
0218-0006
DOI
10.1007/s00026-010-0056-3
language
English
UGent publication?
yes
classification
A1
I have transferred the copyright for this publication to the publisher
id
1105428
handle
http://hdl.handle.net/1854/LU-1105428
date created
2011-01-20 10:02:38
date last changed
2011-02-14 15:18:07
```@article{1105428,
abstract     = {Let e be one of the following full projective embeddings of a finite dual polar space Delta of rank n {\textrangle}= 2: (i) The Grassmann-embedding of the symplectic dual polar space Delta congruent to DW(2n 1,q); (ii) the Grassmann-embedding of the Hermitian dual polar space Delta congruent to DH(2n-1, q(2)); (iii) the spin-embedding of the orthogonal dual polar space Delta congruent to DQ(2n, q); (iv) the spin-embedding of the orthogonal dual polar space Delta congruent to DQ(-)(2n+ 1, q). Let H-e denote the set of all hyperplanes of Delta arising from the embedding e. We give a method for constructing the hyperplanes of H-e without implementing the embedding e and discuss (possible) applications of the given construction.},
author       = {De Bruyn, Bart},
issn         = {0218-0006},
journal      = {ANNALS OF COMBINATORICS},
keyword      = {OVOIDS,FINITE-FIELDS,GENERATION,spin-embedding,Grassmann-embedding,dual polar space,hyperplane},
language     = {eng},
number       = {2},
pages        = {193--209},
title        = {Direct constructions of hyperplanes of dual polar spaces arising from embeddings},
url          = {http://dx.doi.org/10.1007/s00026-010-0056-3},
volume       = {14},
year         = {2010},
}

```
Chicago
De Bruyn, Bart. 2010. “Direct Constructions of Hyperplanes of Dual Polar Spaces Arising from Embeddings.” Annals of Combinatorics 14 (2): 193–209.
APA
De Bruyn, B. (2010). Direct constructions of hyperplanes of dual polar spaces arising from embeddings. ANNALS OF COMBINATORICS, 14(2), 193–209.
Vancouver
1.
De Bruyn B. Direct constructions of hyperplanes of dual polar spaces arising from embeddings. ANNALS OF COMBINATORICS. 2010;14(2):193–209.
MLA
De Bruyn, Bart. “Direct Constructions of Hyperplanes of Dual Polar Spaces Arising from Embeddings.” ANNALS OF COMBINATORICS 14.2 (2010): 193–209. Print.