ISSN:
1420-8997
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract In [9] we proved that the diameter Δ of an Extended partial Geometry (EpG α), of order (s,t) with α ≥2 is bounded by [s/2] −ϕ + 4, where ϕ is the index of the geometry (i.e. the minimum positive antiflag number). An example of EpG2(s,1) with ϕ=α + 1 = 3 attaining the bound is given by a truncated Ds+2 Coxeter complex (see Example 1.2 for a different simple description). In this paper we prove that ifs is even, anEpG α with diameter Δ=[s/2] −ϕ+ 4 〉 3, sayS, has necessarily α = 2,s ≥ 6 andt = 1; if furthermore ϕ=α + 1, thenS is isomorphic to Ds+2. In the cases odd, we give a characterization which still suggests the conjecture that Ds+2 is the unique example (apart from few sporadic cases). The classification of Extended Generalized Quadrangles (EGQ) with maximum diameter was given in [8]. In that case (which correspond to α=1) the unique example (apart from few sporadic cases) was given by the Johnson geometry which can also be described by a truncation of a Coxeter complex of type A2s+1
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01245944
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