The valuations of the near hexagons related to the Witt designsS(5,6,12) andS(5,8,24)

Autor: Bart De Bruyn, Pieter Vandecasteele
Rok vydání: 2006
Předmět:
Zdroj: Journal of Combinatorial Designs. 14:214-228
ISSN: 1520-6610
1063-8539
DOI: 10.1002/jcd.20074
Popis: Valuations of dense near polygons were introduced in 16. In the present paper, we classify all valuations of the near hexagons 1 and 2, which are related to the respective Witt designs S(5,6,12) and S(5,8,24). Using these classifications, we prove that if a dense near polygon S contains a hex H isomorphic to 1 or 2, then H is classical in S. We will use this result to determine all dense near octagons that contain a hex isomorphic to 1 or 2. As a by-product, we obtain a purely geometrical proof for the nonexistence of regular near 2d-gons, d ≥ 4, whose parameters s, t, ti (0 ≤ i ≤ d) satisfy (s, t2, t3) = (2, 1, 11) or (2, 2, 14). The nonexistence of these regular near polygons can also be shown with the aid of eigenvalue techniques. © 2005 Wiley Periodicals, Inc. J Combin Designs 14: 214–228, 2006
Databáze: OpenAIRE
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