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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
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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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Please use this url to cite or link to this publication:

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}},
}

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