Cameron–Fon-Der-Flaass IBIS theorem

In mathematics, Cameron–Fon-Der-Flaass IBIS theorem arises in the dynamical algebraic combinatorics. The theorem was discovered in 1995 by two mathematicians Peter Cameron and Dima Fon-Der-Flaas. The theorem is considered to be a link between group theory and graph theory as it studies redundancy of a group.

Statement

Let $P$ be a permutational group of $\mathrm{\Omega }$,Template:Clarify then the following are equivalent:

• Irredundant bases of $P$ are stored by re-ordering.
• The bases of matroid are formed due to the irredundant bases of $P$.
• Every irredundant base of $P$ got the same size.

Further reading

• https://www.theoremoftheday.org/GroupTheory/IBIS/TotDIBIS.pdf

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