On combinatorial problem, related with fast matrix multiplication
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 13 (2013) no. 4, pp. 63-67.

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The group-theoretical approach to fast matrix multiplication generates specific combinatorial objects, named Uniquely Solvable Puzzles (briefly USP). In the paper some numerical characteristic of the USP was discussed and the relation of USPs to famous combinatorial problem named “Cap set problem” was investigated.
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Yu. V. Kuznetsov. On combinatorial problem, related with fast matrix multiplication. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 13 (2013) no. 4, pp. 63-67. http://geodesic.mathdoc.fr/item/ISU_2013_13_4_a8/

[1] Coppersmith D., Winograd S., “Matrix multiplication via arithmetic progressions”, J. Symbolic Comput., 9:3 (1990), 251–280 | DOI | MR | Zbl

[2] Vassilevska Williams V., “Multiplying Matrices Faster than Coppersmith–Winograd”, Proceedings of the 44-th Symposium on Theory of Computing (STOC'12), 2012, (data obrascheniya 30.09.2013) URL: http://www.cs.berkeley.edu/~virgi/matrixmult-f.pdf

[3] Cohn H., Umans C., “A group theoretic approach to fast matrix multiplication”, Proceedings of the 44-th Annual IEEE Symposium on Foundations of Computer Science, 2003, 438–449

[4] Cohn H., Kleinberg R., Szegedy B., Umans C., “Group-theoretic algorithms for matrix multiplication”, Proceedings of the 46-th Annual IEEE Symposium on Foundations of Computer Science, 2005, 379–388 | DOI

[5] Platonov V. P., Kuznetsov Iu. V., Petrunin M. M., “A group-theoretical approach to the problem of fast matrix multiplication”, Mathematical and computer modeling of systems: theoretical and applied aspects, Collection of scientific papers NIISI RAS, Moscow, 2009, 4–15

[6] Kuznetsov Yu. V., “Some combinatorial aspects of the group-theoretic approach to fast matrix multiplication”, Chebyshevskii sbornik, 13:1 (2012), 102–109 | MR | Zbl

[7] Alon N., Shpilka A., Umans C., “On sunflowers and matrix multiplication”, Electronic Colloquium on Computational Complexity, 2011, Report No 67, 16 pp. | MR

[8] Davis B. L., Maclagan D., “The card game SET”, Mathematical Intelligencer, 25:3 (2003), 33–40 | DOI | MR | Zbl

[9] Bateman M., Katz N., “New bounds on caps sets”, J. American Math. Soc., 25:2 (2012), 585–613 | DOI | MR | Zbl

[10] Edel Y., “Extensions of generalized product caps”, Designs, Codes and Cryptography, 31 (2004), 5–14 | DOI | MR | Zbl

[11] Mebane P., Uniquely Solvable Puzzles and Fast Matrix Multiplication, HMC Senior Theses, 2012, 37 pp.