Glasnik Matematicki, Vol. 40, No.1 (2005), 139-147.

FINITE LINEAR SPACES CONSISTING OF TWO SYMMTRIC CONFIGURATIONS

Vedran Krcadinac and Juraj Siftar

Department of Mathematics, Bijenicka 30, HR-10002 Zagreb, Croatia
e-mail: krcko@math.hr
e-mail: siftar@math.hr

Abstract.   We investigate finite linear spaces consisting of two symmetric configurations. A construction method using projective planes is presented, giving a possibly infinite number of examples. Other examples are constructed by difference families and automorphism groups, including a complete classification of the smallest case. A question whether any Steiner 2-design with twice as many lines as points belongs to this family of linear spaces is raised, and answered in the affirmative for all known examples of such designs.

2000 Mathematics Subject Classification.   51E26, 05B30.

Key words and phrases.   Finite linear space, symmetric configuration.

Full text (PDF) (free access)

DOI: 10.3336/gm.40.1.13

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