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.[1] The theorem is considered to be a link between group theory and graph theory as it studies redundancy of a group.[2][1]
Statement
[edit]Let be a permutational group of ,[clarification needed] then the following are equivalent:
- Irredundant bases of are stored by re-ordering.
- The bases of matroid are formed due to the irredundant bases of .
- Every irredundant base of got the same size.
References
[edit]- ^ a b Patrias, Rebecca; Pechenik, Oliver (2020). "Dynamics of plane partitions: Proof of the Cameron–Fon-Der-Flaass conjecture". Forum of Mathematics, Sigma. 8: 62. arXiv:2003.13152. doi:10.1017/fms.2020.61. ISSN 2050-5094.
- ^ Cameron, P. J; Fon-Der-Flaass, D. G (1995-11-01). "Bases for permutation groups and matroids". European Journal of Combinatorics. 16 (6): 537–544. doi:10.1016/0195-6698(95)90035-7. ISSN 0195-6698.
Further reading
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