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Tag Archives: generalized polygons
Generalized polygons in extremal combinatorics
Jacques Tits invented generalized polygons to give a geometrical interpretation of the exceptional groups of Lie type. The prototype of these incidence geometries already appears in his 1956 paper, while they are axiomatically defined in his influential 1959 paper on … Continue reading
Posted in Combinatorics, Extremal Combinatorics, Finite Geometry, Incidence Geometry, Ramsey Theory, Uncategorized
Tagged extremal problems, generalized polygons, generalized quadrangles, Graph Theory, hypergraphs, John Bamberg, ramsey, ramsey numbers, research, Thomas Lesgourgues, turan problems
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Bounds on Ramsey numbers from finite geometry
In an earlier post I talked about the work of Mubayi and Verstraete on determining the offdiagonal Ramsey numbers via certain optimal pseudorandom graphs, which are not yet known to exist except for the case of triangles. Beyond this conditional … Continue reading
Wenger graphs
A central (and foundational) question in extremal graph theory is the forbidden subgraph problem of Turán, which asks for the largest number of edges in an vertex graph that does not contain any copy of a given graph as its … Continue reading
Generalized hexagons containing a subhexagon
I have recently uploaded a joint paper with Bart, “On generalized hexagons of order and containing a subhexagon”,on arXiv and submitted it for publication. In this work we extend the results of my first paper, which I discussed here, by proving the following: … Continue reading