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Near hexagons with two possible orders for the quads

Bart De Bruyn UGent (2009) Ars Combinatoria. 93. p.225-240
abstract
We study near hexagons which satisfy the following properties: (i) every two points at distance 2 from each other are contained in a unique quad of order $(s,r_1)$ or $(s,r_2)$, \not= r_2$; (ii) every line is contained in the same number of quads; (iii) every two opposite points are connected by the same number of geodesics. We show that there exists an association scheme on the point set of such a near hexagon and calculate the intersection numbers. We also show how the eigenvalues of the collinearity matrix and their corresponding multiplicities can be calculated. The fact that all multiplicities and intersection numbers are nonnegative integers gives restrictions on the parameters of the near hexagon. We apply this to the special case in which the near hexagon has big quads.
Please use this url to cite or link to this publication:
author
organization
year
type
journalArticle (original)
publication status
published
subject
keyword
near hexagon, association scheme, generalized quadrangle, eigenvalue
journal title
Ars Combinatoria
Ars Combin.
volume
93
pages
225 - 240
Web of Science type
Article
Web of Science id
000271166200024
JCR category
MATHEMATICS
JCR impact factor
0.396 (2009)
JCR rank
201/251 (2009)
JCR quartile
4 (2009)
ISSN
0381-7032
language
English
UGent publication?
yes
classification
A1
copyright statement
I don't know the status of the copyright for this publication
id
879280
handle
http://hdl.handle.net/1854/LU-879280
date created
2010-02-24 15:28:29
date last changed
2010-03-05 10:51:27
@article{879280,
  abstract     = {We study near hexagons which satisfy the following properties: (i) every two points at distance 2 from each other are contained in a unique quad of order \$(s,r\_1)\$ or \$(s,r\_2)\$,  {\textbackslash}not= r\_2\$; (ii) every line is contained in the same number of quads; (iii) every two opposite points are connected by the same number of geodesics. We show that there exists an association scheme on the point set of such a near hexagon and calculate the intersection numbers. We also show how the eigenvalues of the collinearity matrix and their corresponding multiplicities can be calculated. The fact that all multiplicities and intersection numbers are nonnegative integers gives restrictions on the parameters of the near hexagon. We apply this to the special case in which the near hexagon has big quads.},
  author       = {De Bruyn, Bart},
  issn         = {0381-7032},
  journal      = {Ars Combinatoria},
  keyword      = {near hexagon,association scheme,generalized quadrangle,eigenvalue},
  language     = {eng},
  pages        = {225--240},
  title        = {Near hexagons with two possible orders for the quads},
  volume       = {93},
  year         = {2009},
}

Chicago
De Bruyn, Bart. 2009. “Near Hexagons with Two Possible Orders for the Quads.” Ars Combinatoria 93: 225–240.
APA
De Bruyn, B. (2009). Near hexagons with two possible orders for the quads. Ars Combinatoria, 93, 225–240.
Vancouver
1.
De Bruyn B. Near hexagons with two possible orders for the quads. Ars Combinatoria. 2009;93:225–40.
MLA
De Bruyn, Bart. “Near Hexagons with Two Possible Orders for the Quads.” Ars Combinatoria 93 (2009): 225–240. Print.