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  • 1
    Electronic Resource
    Electronic Resource
    On multipliers of partial addition sets (1991)
    Springer
    Geometriae dedicata 40 (1991), S. 53-58 
    Details
    ISSN: 1572-9168
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Let G be a finite group not necessarily abelian. We prove a multiplier theorem for a normal partial addition set in G (i.e. a partial addition set which is a union of conjugacy classes).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00181651
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  • 2
    Electronic Resource
    Electronic Resource
    Nets and generalized quadrangles (1994)
    Springer
    Geometriae dedicata 52 (1994), S. 1-14 
    Details
    ISSN: 1572-9168
    Keywords: 51E12 ; 51E14
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract There is a new method of constructing generalized quadrangles (GQs) given by S. Löwe, which is based on covering of nets; all GQs with a regular point can be represented in this way. Here we give a method of constructing GQs with a regular point using the so-called content functions on nets. In the last part of the paper we lay the foundations for a research project aiming to use the more general notion of ‘content’ to classify GQs and maybe to construct new ones.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01263520
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  • 3
    Electronic Resource
    Electronic Resource
    Tubes of even order and flat π.C 2 geometries (1995)
    Springer
    Geometriae dedicata 55 (1995), S. 265-278 
    Details
    ISSN: 1572-9168
    Keywords: Primary: 51E20 ; Secondary 51E24, 05B25
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Atube of even orderq=2 d is a setT={L, $$\mathcal{L}$$ } ofq+3 pairwise skew lines in PG(3,q) such that every plane onL meets the lines of $$\mathcal{L}$$ in a hyperoval. Thequadric tube is obtained as follows. Take a hyperbolic quadricQ=Q 3 + (q) in PG(3,q); letL be an exterior line, and let $$\mathcal{L}$$ consist of the polar line ofL together with a regulus onQ. In this paper we show the existence of tubes of even order other than the quadric one, and we prove that the subgroup of PГL(4,q) fixing a tube {L, $$\mathcal{L}$$ } cannot act transitively on $$\mathcal{L}$$ . As pointed out by a construction due to Pasini, this implies new results for the existence of flat π.C 2 geometries whoseC 2-residues are nonclassical generalized quadrangles different from nets. We also give the results of some computations on the existence and uniqueness of tubes in PG(3,q) for smallq. Further, we define tubes for oddq (replacing ‘hyperoval’ by ‘conic’ in the definition), and consider briefly a related extremal problem.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01266318
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    Regular groups on generalized quadrangles and nonabelian difference sets with multiplier -1 (1992)
    Springer
    Geometriae dedicata 41 (1992), S. 165-174 
    Details
    ISSN: 1572-9168
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This is a first approach to the study of regular generalized quadrangles (i.e. generalized quadrangles with an automorphism group sharply 1-transitive on points). In this paper we point out how the problem is connected to the theory of difference sets with multiplier-1. First, some of the results in [3] on difference sets with multiplier-1 are extended to the nonabelian case; then, these new results on difference sets are used to prove nonexistence theorems for regular GQs of even order s=t.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00182417
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  • 5
    Electronic Resource
    Electronic Resource
    Extended partial geometries with minimal μ (1992)
    Springer
    Geometriae dedicata 42 (1992), S. 119-128 
    Details
    ISSN: 1572-9168
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Recently Fisher and Hobart extended the original work of Buekenhout and Hubaut on extended generalized quadrangles with a certain minimal value (‘minimal μ’) for the nonempty residue intersections. We show that there is another minimal μ which is sometimes better than the earlier one, and we extend all this to the case of extended partial geometries. We examine especially the triangular case, and find only a few new possibilities, which we are unable to settle, although some of these look extremely interesting.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00147543
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  • 6
    Electronic Resource
    Electronic Resource
    The Steinberg module of a graph (1990)
    Springer
    Archiv der Mathematik 55 (1990), S. 503-506 
    Details
    ISSN: 1420-8938
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01190273
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  • 7
    Electronic Resource
    Electronic Resource
    TruncatedD n coxeter complexes as extended partial geometries with maximum diameter (1992)
    Springer
    Journal of geometry 43 (1992), S. 75-94 
    Details
    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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