SEMINAR: Groups and Combinatorics Seminar: Regular near hexagons and Qpolynomial distanceregular graphs


Groups and Combinatorics Seminar: Regular near hexagons and Qpolynomial distanceregular graphs 
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Time and place: 15:00 Friday 24 April in Blakers LT.
Speaker: Bart De Bruyn (Ghent University)
Title: Regular near hexagons and Qpolynomial distanceregular graphs.
Abstract: A near 2dgon is a pointline geometry with diameter d having the property that for every point x and every line L, there exists a unique point on L nearest to x. A near polygon is called thick if every line is incident with at least three points and regular if its collinearity graph is a socalled distanceregular graph. In my talk, I will discuss thick regular near 2dgons with a socalled Qpolynomial collinearity graph. For d > 3, we show that apart from Hamming near polygons and dual polar spaces there are no thick Qpolynomial regular near polygons. A thick regular near hexagon is Qpolynomial if and only if t = s^3 + t_2 (s^2  s + 1), where t + 1 is the number of lines through each point, s + 1 is the number of points on each line and t_2 + 1 is the constant number of common neighbors that two points at distance 2 have. We also show that there cannot exist (necessarily Qpolynomial) regular near hexagons whose parameters (s,t_2,t) are equal to either (3,1,34), (8,4,740), (92,64,1314560), (95,19,1027064) or (105,147,2763012). All these nonexistence results imply the nonexistence of distanceregular graphs with certain parameters. We also mention some applications of these nonexistence results.
(Joint work with Frederic Vanhove)
Contact 
Gabriel Verret
<[email protected]>

Start 
Fri, 24 Apr 2015 15:00

End 
Fri, 24 Apr 2015 16:00

Submitted by 
Gabriel Verret <[email protected]>

Last Updated 
Tue, 21 Apr 2015 08:51

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