On the intersection of distance-$j$-ovoids and subpolygons in generalized polygons
- Author
- Bart De Bruyn (UGent)
- Organization
- 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'$. We derive a similar result for the intersection of distance-2-ovoids and suboctagons of generalized octagons.
- Keywords
- distance-$j$-ovoid, ovoid, generalized polygon, left-regular partition, right-regular partition, subpolygon
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Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-879245
- MLA
- De Bruyn, Bart. “On the Intersection of Distance-$j$-Ovoids and Subpolygons in Generalized Polygons.” Discrete Mathematics, vol. 309, 2009, pp. 3023–31.
- APA
- De Bruyn, B. (2009). On the intersection of distance-$j$-ovoids and subpolygons in generalized polygons. Discrete Mathematics, 309, 3023–3031.
- Chicago author-date
- De Bruyn, Bart. 2009. “On the Intersection of Distance-$j$-Ovoids and Subpolygons in Generalized Polygons.” Discrete Mathematics 309: 3023–31.
- Chicago author-date (all authors)
- De Bruyn, Bart. 2009. “On the Intersection of Distance-$j$-Ovoids and Subpolygons in Generalized Polygons.” Discrete Mathematics 309: 3023–3031.
- Vancouver
- 1.De Bruyn B. On the intersection of distance-$j$-ovoids and subpolygons in generalized polygons. Discrete Mathematics. 2009;309:3023–31.
- IEEE
- [1]B. De Bruyn, “On the intersection of distance-$j$-ovoids and subpolygons in generalized polygons,” Discrete Mathematics, vol. 309, pp. 3023–3031, 2009.
@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'$. We derive a similar result for the intersection of distance-2-ovoids and suboctagons of generalized octagons.}}, author = {{De Bruyn, Bart}}, issn = {{0012-365X}}, journal = {{Discrete Mathematics}}, keywords = {{distance-$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}}, }