### Near hexagons with two possible orders for the quads

(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:
http://hdl.handle.net/1854/LU-879280

- author
- Bart De Bruyn UGent
- organization
- year
- 2009
- 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.