### On the intersection of distance-$j$-ovoids and subpolygons in generalized polygons

(2009) Discrete Mathematics. 309. p.3023-3031- abstract
- De Wispelaere and Van Maldeghem gave a technique for calculating the intersection sizes of combinatorial substructures associated with regular partitions of distance-regular graphs. This technique was based on the orthogonality of the eigenvectors which correspond to distinct eigenvalues of the (symmetric) adjacency matrix. In the present paper, we give a more general method for calculating intersection sizes of combinatorial structures. The proof of this method is based on the solution of a linear system of equations which is obtained by means of double countings. We also give a new class of regular partitions of generalized hexagons and determine under which conditions ovoids and subhexagons of order $(s',t')$ of a generalized hexagon of order $ intersect in a constant number of points. If the automorphism group of the generalized hexagon is sufficiently large, then this is the case if and only if =s't'$. We derive a similar result for the intersection of distance-2-ovoids and suboctagons of generalized octagons.

Please use this url to cite or link to this publication:
http://hdl.handle.net/1854/LU-879245

- author
- De Bruyn, Bart UGent
- organization
- alternative title
- On the intersection of distance-j-ovoids and subpolygons of generalized polygons
- year
- 2009
- type
- journalArticle (original)
- publication status
- published
- subject
- keyword
- distance-$j$-ovoid, ovoid, generalized polygon, left-regular partition, right-regular partition, subpolygon
- journal title
- Discrete Mathematics
- Discrete Math.
- volume
- 309
- pages
- 3023 - 3031
- Web of Science type
- Article
- Web of Science id
- 000266654300009
- JCR category
- MATHEMATICS
- JCR impact factor
- 0.548 (2009)
- JCR rank
- 158/251 (2009)
- JCR quartile
- 3 (2009)
- ISSN
- 0012-365X
- language
- English
- UGent publication?
- yes
- classification
- A1
- copyright statement
*I don't know the status of the copyright for this publication*- id
- 879245
- handle
- http://hdl.handle.net/1854/LU-879245
- date created
- 2010-02-24 15:05:55
- date last changed
- 2016-12-19 15:46:37

@article{879245, abstract = {De Wispelaere and Van Maldeghem gave a technique for calculating the intersection sizes of combinatorial substructures associated with regular partitions of distance-regular graphs. This technique was based on the orthogonality of the eigenvectors which correspond to distinct eigenvalues of the (symmetric) adjacency matrix. In the present paper, we give a more general method for calculating intersection sizes of combinatorial structures. The proof of this method is based on the solution of a linear system of equations which is obtained by means of double countings. We also give a new class of regular partitions of generalized hexagons and determine under which conditions ovoids and subhexagons of order \$(s',t')\$ of a generalized hexagon of order \$ intersect in a constant number of points. If the automorphism group of the generalized hexagon is sufficiently large, then this is the case if and only if =s't'\$. We derive a similar result for the intersection of distance-2-ovoids and suboctagons of generalized octagons.}, author = {De Bruyn, Bart}, issn = {0012-365X}, journal = {Discrete Mathematics}, keyword = {distance-\$j\$-ovoid,ovoid,generalized polygon,left-regular partition,right-regular partition,subpolygon}, language = {eng}, pages = {3023--3031}, title = {On the intersection of distance-\$j\$-ovoids and subpolygons in generalized polygons}, volume = {309}, year = {2009}, }

- Chicago
- De Bruyn, Bart. 2009. “On the Intersection of Distance-$j$-ovoids and Subpolygons in Generalized Polygons.”
*Discrete Mathematics*309: 3023–3031. - APA
- De Bruyn, B. (2009). On the intersection of distance-$j$-ovoids and subpolygons in generalized polygons.
*Discrete Mathematics*,*309*, 3023–3031. - Vancouver
- 1.De Bruyn B. On the intersection of distance-$j$-ovoids and subpolygons in generalized polygons. Discrete Mathematics. 2009;309:3023–31.
- MLA
- De Bruyn, Bart. “On the Intersection of Distance-$j$-ovoids and Subpolygons in Generalized Polygons.”
*Discrete Mathematics*309 (2009): 3023–3031. Print.