Toida's conjecture - Alchetron, The Free Social Encyclopedia

In combinatorial mathematics, Toida's conjecture, due to Shunichi Toida in 1977, is a refinement of the disproven Ádám's conjecture in 1967. Toida's conjecture states formally:

If

S is a subset of Z n ∗

and

X → = X → ( Z n ; S )

then X → is a CI-digraph.

Proofs

The conjecture was proven in the special case where n is a prime power by Klin and Poschel in 1978, and by Golfand, Najmark, and Poschel in 1984.

The conjecture was then fully proven by Muzychuk, Klin, and Poschel in 2001 by using Schur algebra, and simultaneously by Dobson and Morris in 2002 by using the classification of finite simple groups.

References

Toida's conjecture Wikipedia

(Text) CC BY-SA