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 Von-Der-Flaass. The theorem is considered to be a link between group theory and graph theory as it studies redundancy of a group.

Let ${\displaystyle P}$be a permutational group of ${\displaystyle \Omega }$,^{[clarification needed]} then the following are equivalent:

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

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