Prékopa–Leindler inequality

From formulasearchengine
Jump to navigation Jump to search

In abstract algebra, the triple product property is an identity satisfied in some groups.

Let G be a non-trivial group. Three nonempty subsets S,T,UG are said to have the triple product property in G if for all elements s,sS, t,tT, u,uU it is the case that

ss1tt1uu1=1s=s,t=t,u=u

where 1 is the identity of G.

It plays a role in research of fast matrix multiplication algorithms.

References

  • Henry Cohn, Chris Umans. A Group-theoretic Approach to Fast Matrix Multiplication. Template:Arxiv. Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science, 11–14 October 2003, Cambridge, MA, IEEE Computer Society, pp. 438–449.

See also