On automorphism group of a possible short algorithm for multiplication of $3\times3$ matrices
Abstract
Studying algorithms admitting nontrivial symmetries is a prospective way of constructing new short algorithms of matrix multiplication. The main result of the article is that if there exists an algorithm of multiplicative length $l\leq22$ for multuplication of $3\times3$ matrices then its automorphism group is isomorphic to a subgroup of $S_l\times S_3$.
- Publication:
-
arXiv e-prints
- Pub Date:
- November 2022
- DOI:
- 10.48550/arXiv.2211.06485
- arXiv:
- arXiv:2211.06485
- Bibcode:
- 2022arXiv221106485B
- Keywords:
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- Computer Science - Computational Complexity;
- Mathematics - Group Theory;
- 68Q25 (Primary);
- 20C99 (Secondary);
- F.2
- E-Print:
- 11 pp. To be submitted to European J. Math