View source for Fisher inequality

{{MSC|05B05}}

A constraint on the parameters of a [[balanced incomplete block design]].  A BIBD is an [[incidence system]] on a set $V$ of $v$ points and a family $B$ of $b$ blocks: subsets of points, each of size $k$.  It is required that each point be contained in just $r$ blocks and each pair of points in just $\lambda$ blocks.

Fisher's inequality states that
$$
b \ge v \ .
$$

A ''[[symmetric design]]'' is one in which equality holds: $b = v$.

====References====
* Hall, M. jr, ''Combinatorial theory'' Blaisdell (1967) {{ZBL|0196.02401}}

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