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

Bart De Bruyn UGent (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'$. We derive a similar result for the intersection of distance-2-ovoids and suboctagons of generalized octagons.
Please use this url to cite or link to this publication:
author
organization
alternative title
On the intersection of distance-j-ovoids and subpolygons of generalized polygons
year
type
journalArticle (original)
publication status
published
subject
keyword
distance-$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
2010-03-05 09:46:08
@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.