Geodesic
Non-existence of a short algorithm for multiplication of $3\times 3$ matrices whose group is $S_4\times S_3$, II
Trudy Instituta matematiki, Tome 31 (2023) no. 1, pp. 101-111 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

It is proved that there is no algorithm for multiplication of $3\times 3$ matrices of multiplicative length $\leqslant 23$ that is invariant under a certain group isomorphic to $S_4\times S_3$. The proof uses description of the orbits of this group on decomposable tensors in the tensor cube $(M_3(\mathbb{C}))^{\otimes 3}$ which was obtained earlier. 
@article{TIMB_2023_31_1_a11,
     author = {V. P. Burichenko},
     title = {Non-existence of a short algorithm for multiplication of $3\times 3$ matrices whose group is $S_4\times S_3${,~II}},
     journal = {Trudy Instituta matematiki},
     pages = {101--111},
     year = {2023},
     volume = {31},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TIMB_2023_31_1_a11/}
}
TY  - JOUR
AU  - V. P. Burichenko
TI  - Non-existence of a short algorithm for multiplication of $3\times 3$ matrices whose group is $S_4\times S_3$, II
JO  - Trudy Instituta matematiki
PY  - 2023
SP  - 101
EP  - 111
VL  - 31
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TIMB_2023_31_1_a11/
LA  - en
ID  - TIMB_2023_31_1_a11
ER  - 
%0 Journal Article
%A V. P. Burichenko
%T Non-existence of a short algorithm for multiplication of $3\times 3$ matrices whose group is $S_4\times S_3$, II
%J Trudy Instituta matematiki
%D 2023
%P 101-111
%V 31
%N 1
%U http://geodesic.mathdoc.fr/item/TIMB_2023_31_1_a11/
%G en
%F TIMB_2023_31_1_a11
V. P. Burichenko. Non-existence of a short algorithm for multiplication of $3\times 3$ matrices whose group is $S_4\times S_3$, II. Trudy Instituta matematiki, Tome 31 (2023) no. 1, pp. 101-111. http://geodesic.mathdoc.fr/item/TIMB_2023_31_1_a11/

[1] V. P. Burichenko, “Non-existence of a short algorithm for multiplication of $3\times 3$ matrices with group $S_x\times S_3$”, Tr. In-ta matematiki [Proceedings of the Institute of mathematics], 30:1-2 (2022), 99–116

[2] V. P. Burichenko, Symmetries of matrix multiplication algorithms. I, 2015, arXiv: 1508.01110 | Zbl

[3] V. P. Burichenko, “The isotropy group of the matrix multiplication tensor”, Tr. In-ta matematiki [Proceedings of the Institute of mathematics], 24:2 (2016), 106–118 | MR

[4] R. P. Brent, Algorithms for matrix multiplication, Technical report 70–157, Stanford university, Computer Science Department, 1970 http://maths-people.anu.edu.au/brent/pub/pub002.html