Geodesic
Schur rings over the elementary abelian group of order~$64$
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 14 (2017), pp. 443-450.

Voir la notice de l'article provenant de la source Math-Net.Ru

We report on the classification of S-rings over the group $E_{64}$ up to scheme isomorphism. A total of $2082$ schemes were found.
Keywords: commutative group, algebra. 
@article{SEMR_2017_14_a13,
     author = {S. Reichard},
     title = {Schur rings over the elementary abelian group of order~$64$},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {443--450},
     publisher = {mathdoc},
     volume = {14},
     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2017_14_a13/}
}
TY  - JOUR
AU  - S. Reichard
TI  - Schur rings over the elementary abelian group of order~$64$
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2017
SP  - 443
EP  - 450
VL  - 14
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SEMR_2017_14_a13/
LA  - en
ID  - SEMR_2017_14_a13
ER  - 
%0 Journal Article
%A S. Reichard
%T Schur rings over the elementary abelian group of order~$64$
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2017
%P 443-450
%V 14
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SEMR_2017_14_a13/
%G en
%F SEMR_2017_14_a13
S. Reichard. Schur rings over the elementary abelian group of order~$64$. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 14 (2017), pp. 443-450. http://geodesic.mathdoc.fr/item/SEMR_2017_14_a13/

[1] E. Bannai, T. Ito, Algebraic Combinatorics, v. I, Association schemes, The Benjamin/Cummings Publishing Co., Inc., Menlo Park CA, 1984 | MR | Zbl

[2] I. A. Faradžev, M. H. Klin, M. E. Muzichuk, “Cellular rings and groups of automorphisms of graphs”, Investigations in algebraic theory of combinatorial objects, Math. Appl. (Soviet Ser.), 84, eds. I. A. Faradzhev et al., Kluwer Acad. Publ., Dordrecht, 1994, 1–152 | MR | Zbl

[3] GAP — Groups, Algorithms, and Programming, Version 4.7.8, , The GAP Group, 2015 http://www.gap-system.org

[4] A. Hanaki, P.-H. Zieschang, “On imprimitive noncommutative association schemes of order $6$”, Commun. Algebra, 42:3 (2014), 1151–1199 | DOI | MR | Zbl

[5] M. Muzychuk, I. Ponomarenko, “Schur rings”, Eur. J. Comb., 30:6 (2009), 1526–1539 | DOI | MR | Zbl

[6] P. Christian, S. Reichard, “Enumerating set orbits”, Algorithmic Algebraic Combinatorics and Gröbner Bases, eds. M. Klin et al., Springer, Dordrecht, 2009, 137–150 | MR | Zbl

[7] R. C. Read, “Every one a winner, or how to avoid isomorphism search when cataloguing combinatorial configurations”, Ann. Discrete Math., 2 (1978), 107–120 | DOI | MR | Zbl

[8] S. Reichard, Schur rings over ${E}_{64}$, , 2016 http://www.math.tu-dresden.de/r̃eichard/schur/e64/

[9] I. Schur, “Zur Theorie der einfach transitiven Permutationsgruppen”, Sitzungsber. Preuss. Akad. Wiss., Phys.-Math. Kl., 1933:18–20 (1933), 598–623

[10] B. Weisfeiler (ed.), On Construction and Identification of Graphs, Lecture Notes in Mathematics, 558, Springer-Verlag, Berlin–Heidelberg–New York, 1976 | DOI | MR | Zbl

[11] H. Wielandt, Finite permutation groups, Academic Press, New York–London, 1964 | MR | Zbl

[12] M. Ziv-Av, “Enumeration of Schur rings over small groups”, Computer Algebra in Scientific Computing, 16th Int. Workshop, CASC 2014 (Warsaw, Poland, September 8–12, 2014), Lecture Notes in Computer Science, 8660, eds. V. P. Gerdt et al., 2014, 491–500 | DOI | Zbl