Bose theorem

The set of Bose (by Raj Chandra Bose ) is an inequality in the combinatorics and in the finite geometry is of importance. It describes a relationship between different parameters in a structure called a block diagram and also provides a necessary criterion for their existence for a given combination of parameters. This means that if a parameter combination does not satisfy the inequality, the associated block diagram does not exist.

The inequality describes in which relationship

the number of points v ,

the number of blocks b and

the number r of blocks by one, i.e. every point

a block plan . It represents an exacerbation of the Fisher inequality for block plans with parallelisms. ${\displaystyle 2{\text{-}}(v,k,\lambda )}$

For every block diagram D that has a parallelism , the following applies: ${\displaystyle 2{\text{-}}(v,k,\lambda )}$

${\displaystyle b\geq v+r-1}$and is affine. ${\displaystyle b=v+r-1\Leftrightarrow }$ ${\displaystyle D}$

So equality exists if and only if the block diagram is affine .

literature

• A. Beutelspacher : Introduction to finite geometry I . P. 47, Bibliographisches Institut 1983, ISBN 3-411-01648-5