# Fisher inequality

From Encyclopedia of Mathematics

2020 Mathematics Subject Classification: *Primary:* 05B05 [MSN][ZBL]

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

**How to Cite This Entry:**

Fisher inequality.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Fisher_inequality&oldid=37365