On cap sets and the group-theoretic approach to matrix multiplication
نویسندگان
چکیده
In 2003, Cohn and Umans described a framework for proving upper bounds on the exponent ω of matrix multiplication by reducing matrix multiplication to group algebra multiplication. In 2005 Cohn, Kleinberg, Szegedy, and Umans proposed specific conjectures for how to obtain ω = 2 in this framework. In this note we rule out obtaining ω = 2 in this framework from the groups Fp , using the breakthrough results of Croot, Lev, Pach, Ellenberg, and Gijswijt on cap sets. These restrictions do not however rule out abelian groups in general, let alone nonabelian groups.
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عنوان ژورنال:
- CoRR
دوره abs/1605.06702 شماره
صفحات -
تاریخ انتشار 2016