### Hyperplanes of DW(5,K) with K a perfect field of characteristic 2

(2009) JOURNAL OF ALGEBRAIC COMBINATORICS. 30(4). p.567-584- abstract
- Let K be a perfect field of characteristic 2. In this paper, we classify all hyperplanes of the symplectic dual polar space DW(5, K) that arise from its Grassmann embedding. We show that the number of isomorphism classes of such hyperplanes is equal to 5 + N, where N is the number of equivalence classes of the following equivalence relation R on the set {lambda is an element of K|X(2) + lambda X + 1 is irreducible in K[X]}: (lambda(1), lambda(2)) is an element of R whenever there exists an automorphism sigma of K and an a is an element of K such that (lambda(sigma)(2))(-1) = lambda(-1)(1) + a(2) + a.

Please use this url to cite or link to this publication:
http://hdl.handle.net/1854/LU-879954

- author
- Bart De Bruyn UGent
- organization
- alternative title
- Hyperplanes of DW(5, K) with K a perfect field of characteristic 2
- year
- 2009
- type
- journalArticle (original)
- publication status
- published
- subject
- keyword
- perfect field, symplectic dual polar space, hyperplane, DUAL POLAR SPACES, EMBEDDINGS, RANK-3, ARISE
- journal title
- JOURNAL OF ALGEBRAIC COMBINATORICS
- J. Algebr. Comb.
- volume
- 30
- issue
- 4
- pages
- 567 - 584
- Web of Science type
- Article
- Web of Science id
- 000271502700010
- JCR category
- MATHEMATICS
- JCR impact factor
- 1.137 (2009)
- JCR rank
- 38/251 (2009)
- JCR quartile
- 1 (2009)
- ISSN
- 0925-9899
- DOI
- 10.1007/s10801-009-0180-5
- language
- English
- UGent publication?
- yes
- classification
- A1
- copyright statement
*I have transferred the copyright for this publication to the publisher*- id
- 879954
- handle
- http://hdl.handle.net/1854/LU-879954
- date created
- 2010-02-24 16:58:22
- date last changed
- 2014-01-28 19:18:23

@article{879954, abstract = {Let K be a perfect field of characteristic 2. In this paper, we classify all hyperplanes of the symplectic dual polar space DW(5, K) that arise from its Grassmann embedding. We show that the number of isomorphism classes of such hyperplanes is equal to 5 + N, where N is the number of equivalence classes of the following equivalence relation R on the set \{lambda is an element of K|X(2) + lambda X + 1 is irreducible in K[X]\}: (lambda(1), lambda(2)) is an element of R whenever there exists an automorphism sigma of K and an a is an element of K such that (lambda(sigma)(2))(-1) = lambda(-1)(1) + a(2) + a.}, author = {De Bruyn, Bart}, issn = {0925-9899}, journal = {JOURNAL OF ALGEBRAIC COMBINATORICS}, keyword = {perfect field,symplectic dual polar space,hyperplane,DUAL POLAR SPACES,EMBEDDINGS,RANK-3,ARISE}, language = {eng}, number = {4}, pages = {567--584}, title = {Hyperplanes of DW(5,K) with K a perfect field of characteristic 2}, url = {http://dx.doi.org/10.1007/s10801-009-0180-5}, volume = {30}, year = {2009}, }

- Chicago
- De Bruyn, Bart. 2009. “Hyperplanes of DW(5,K) with K a Perfect Field of Characteristic 2.”
*Journal of Algebraic Combinatorics*30 (4): 567–584. - APA
- De Bruyn, B. (2009). Hyperplanes of DW(5,K) with K a perfect field of characteristic 2.
*JOURNAL OF ALGEBRAIC COMBINATORICS*,*30*(4), 567–584. - Vancouver
- 1.De Bruyn B. Hyperplanes of DW(5,K) with K a perfect field of characteristic 2. JOURNAL OF ALGEBRAIC COMBINATORICS. 2009;30(4):567–84.
- MLA
- De Bruyn, Bart. “Hyperplanes of DW(5,K) with K a Perfect Field of Characteristic 2.”
*JOURNAL OF ALGEBRAIC COMBINATORICS*30.4 (2009): 567–584. Print.