Journal ArticleDOI
Some combinatorial and geometric characterizations of the finite dual classical generalized hexagons
TLDR
In this article, the dual of a generalized hexagon Γ of finite order (s, t) is associated to the Chevalley groups if and only if the intersection of any two tracesxy andxz, with some additional condition, contains at mostt/s + 1 elements.Abstract:
We characterize the dual of the generalized hexagons naturally associated to the groupsG2(q) and3D4(q) by looking at certain configurations, and also by considering intersections of traces. For instance, the dual of a generalized hexagon Γ of finite order (s, t) is associated to the Chevalley groups mentioned above if and only if the intersection of any two tracesxy andxz, with some additional condition, contains at mostt/s + 1 elements.read more
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Posted Content
A note on Pseudorandom Ramsey graphs.
Dhruv Mubayi,Jacques Verstraëte +1 more
TL;DR: It is proved that if optimal $K_s$-free pseudorandom graphs exist, then the Ramsey number r(s,t) = t^{s-1+o(1}$ as $t \rightarrow \infty$ as well as improving the exponent of $t$ over the bounds given by the random $F$- free process and random graphs.
Journal ArticleDOI
Full Embeddings Of The Finite Dual Split Cayley Hexagons
A. Thas,H. Van Maldeghem +1 more
TL;DR: For each prime power q, given an embedding of the finite dual split Cayley hexagon H(q)D in the d-dimensional projective space PG(d, q), d satisfies d ≤ 13, and if d = 13, then the embedding is unique and the description is given.
Journal ArticleDOI
Some Remarks on Steiner Systems
TL;DR: It is shown that the blocks of the Steiner systems can take the blocks amongst the lines and the traces of the hexagon, and some facts about the automorphism groups are proved.
Journal ArticleDOI
A note on multicolor Ramsey number of small odd cycles versus a large clique
TL;DR: In this article , the lower bound for Rk(H;Km) when H is C5 or C7 was shown to be Ω(m3k8+1/(log Ωm)3k 8+1).
References
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Book ChapterDOI
Chapter 9 – Generalized Polygons
TL;DR: In this paper, the authors introduce some basic notions on finite generalized polygons and state important restrictions on the parameters, including the Feit-Higman theorem, and describe the unique properties of generalized quadrangles with small parameters, such as ovoids, spreads, polarities, and subpolygons.