### The nonexistence of regular near octagons with parameters (s, t, t(2), t(3)) = (2,24,0,8)

(2010) ELECTRONIC JOURNAL OF COMBINATORICS. 17(1).- abstract
- Let S be a regular near octagon with s + 1 = 3 points per line, let t + 1 denote the constant number of lines through a given point of S and for every two points x and y at distance i is an element of {2, 3} from each other, let t(i) + 1 denote the constant number of lines through y containing a (necessarily unique) point at distance i - 1 from x. It is known, using algebraic combinatorial techniques, that (t(2), t(3), t) must be equal to either (0, 0, 1), (0, 0, 4), (0, 3, 4), (0, 8, 24), (1, 2, 3), (2, 6, 14) or (4, 20, 84). For all but one of these cases, there is a unique example of a regular near octagon known. In this paper, we deal with the existence question for the remaining case. We prove that no regular near octagons with parameters (s, t, t(2), t(3)) = (2, 24, 0, 8) can exist.

Please use this url to cite or link to this publication:
http://hdl.handle.net/1854/LU-1108479

- author
- Bart De Bruyn UGent
- organization
- year
- 2010
- type
- journalArticle (original)
- publication status
- published
- subject
- keyword
- INEQUALITY, POLYGONS, THICK
- journal title
- ELECTRONIC JOURNAL OF COMBINATORICS
- Electron. J. Comb.
- volume
- 17
- issue
- 1
- article_number
- R149
- Web of Science type
- Article
- Web of Science id
- 000283858000002
- JCR category
- MATHEMATICS
- JCR impact factor
- 0.626 (2010)
- JCR rank
- 124/276 (2010)
- JCR quartile
- 2 (2010)
- ISSN
- 1077-8926
- language
- English
- UGent publication?
- yes
- classification
- A1
- copyright statement
*I have retained and own the full copyright for this publication*- id
- 1108479
- handle
- http://hdl.handle.net/1854/LU-1108479
- alternative location
- http://www.combinatorics.org/Volume_17/PDF/v17i1r149.pdf
- date created
- 2011-01-22 10:17:46
- date last changed
- 2011-02-09 10:04:08

@article{1108479, abstract = {Let S be a regular near octagon with s + 1 = 3 points per line, let t + 1 denote the constant number of lines through a given point of S and for every two points x and y at distance i is an element of \{2, 3\} from each other, let t(i) + 1 denote the constant number of lines through y containing a (necessarily unique) point at distance i - 1 from x. It is known, using algebraic combinatorial techniques, that (t(2), t(3), t) must be equal to either (0, 0, 1), (0, 0, 4), (0, 3, 4), (0, 8, 24), (1, 2, 3), (2, 6, 14) or (4, 20, 84). For all but one of these cases, there is a unique example of a regular near octagon known. In this paper, we deal with the existence question for the remaining case. We prove that no regular near octagons with parameters (s, t, t(2), t(3)) = (2, 24, 0, 8) can exist.}, articleno = {R149}, author = {De Bruyn, Bart}, issn = {1077-8926}, journal = {ELECTRONIC JOURNAL OF COMBINATORICS}, keyword = {INEQUALITY,POLYGONS,THICK}, language = {eng}, number = {1}, title = {The nonexistence of regular near octagons with parameters (s, t, t(2), t(3)) = (2,24,0,8)}, url = {http://www.combinatorics.org/Volume\_17/PDF/v17i1r149.pdf}, volume = {17}, year = {2010}, }

- Chicago
- De Bruyn, Bart. 2010. “The Nonexistence of Regular Near Octagons with Parameters (s, T, T(2), T(3)) = (2,24,0,8).”
*Electronic Journal of Combinatorics*17 (1). - APA
- De Bruyn, B. (2010). The nonexistence of regular near octagons with parameters (s, t, t(2), t(3)) = (2,24,0,8).
*ELECTRONIC JOURNAL OF COMBINATORICS*,*17*(1). - Vancouver
- 1.De Bruyn B. The nonexistence of regular near octagons with parameters (s, t, t(2), t(3)) = (2,24,0,8). ELECTRONIC JOURNAL OF COMBINATORICS. 2010;17(1).
- MLA
- De Bruyn, Bart. “The Nonexistence of Regular Near Octagons with Parameters (s, T, T(2), T(3)) = (2,24,0,8).”
*ELECTRONIC JOURNAL OF COMBINATORICS*17.1 (2010): n. pag. Print.