In mathematics, Cameron–Fon-Der-Flaass IBIS theorem arises in the dynamical

algebraic combinatorics Algebraic combinatorics is an area of mathematics that employs methods of abstract algebra, notably group theory and representation theory, in various combinatorial contexts and, conversely, applies combinatorial techniques to problems in algeb ...

. The theorem was discovered in 1995 by two mathematicians

Peter Cameron Peter Cameron may refer to: * Peter Cameron (entomologist) (1847–1912), English entomologist who specialised in Hymenoptera * Peter Cameron (mathematician) (born 1947), Australian mathematician, joint winner of the 2003 Euler Medal * Peter Camero ...

and Dima Von-Der-Flaass. The theorem is considered to be a link between

group theory In abstract algebra, group theory studies the algebraic structures known as group (mathematics), groups. The concept of a group is central to abstract algebra: other well-known algebraic structures, such as ring (mathematics), rings, field ( ...

and

graph theory In mathematics and computer science, graph theory is the study of ''graph (discrete mathematics), graphs'', which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of ''Vertex (graph ...

as it studies redundancy of a group.

Statement

Let

P

be a permutational group of

\Omega

, then the following are equivalent: * Irredundant bases of

P

are stored by re-ordering. * The bases of

matroid In combinatorics, a matroid is a structure that abstracts and generalizes the notion of linear independence in vector spaces. There are many equivalent ways to define a matroid Axiomatic system, axiomatically, the most significant being in terms ...

are formed due to the irredundant bases of

P

. * Every irredundant base of

P

got the same size.

Statement

References

Further reading