#### 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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CrossRef

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*A new Steiner S(2,5,41) design (summary)*,
2nd Croatian Congress of Mathematics, Croatian
Mathematical Society, 2000, pp. 52.

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