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Steiner System

A Steiner system is a set $X$ of $v$ points, and a collection of subsets of $X$ of size $k$ (called blocks), such that any $t$ points of $X$ are in exactly one of the blocks. The special case $t=2$ and $k=3$ corresponds to a so-called Steiner Triple System. For a Projective Plane, $v=n^2+n+1$, $k=n+1$, $t=2$, and the blocks are simply lines.

See also Steiner Quadruple System, Steiner Triple System.


Colbourn, C. J. and Dinitz, J. H. (Eds.) CRC Handbook of Combinatorial Designs. Boca Raton, FL: CRC Press, 1996.

Woolhouse, W. S. B. ``Prize Question 1733.'' Lady's and Gentleman's Diary. 1844.

© 1996-9 Eric W. Weisstein