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

Bart De Bruyn UGent (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:
author
organization
year
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.