Abstract
A Cameron-Liebler line class is a set L of lines in PG(3, q) for which there exists a number x such that |L⋂S|=x for all spreads S. There are many equivalent properties: Theorem 1 lists eight. This paper classifies Cameron-Liebler line classes with x⩽4 (with two exceptions). It is also shown that the study of Cameron-Liebler line classes is equivalent to the study of weighted sets of points in PG(3, q) with two weights on lines.
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References
R.H. Bruck ‘Construction problems of finite projective planes’, in, R.C. Bose and T.A. Dowling (eds), Combinatorial Mathematics and its Applications, Univ. of North Carolina Press, Chapel Hill, 1969.
P.J. Cameron and R.A. Liebler, ‘Tactical decompositions and orbits of projective groups, Lin. Alg. Appl. 46 (1982), 91–102.
E. d'Agostini, ‘On the characterisation of (k, n; f)-caps of type (n−2, n)’, Atti. Sem. Mat. Fis. Univ. Modena 29 (1980), 263–275.
M. Tallini Scafati, ‘Calotte di tipo (m, n) in uno spazio di Galois S r,q ’, Rend. Acc. Naz. Lincei (8) 53 (1972), 71–81.
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Penttila, T. Cameron-Liebler line classes in PG (3,q). Geom Dedicata 37, 245–252 (1991). https://doi.org/10.1007/BF00181401
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DOI: https://doi.org/10.1007/BF00181401