Geodesic
On T-amorphous association schemes
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 31, Tome 455 (2017), pp. 98-121 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

A scheme is called T-amorphous if it is antisymmetric and any tournament obtained by an appropriate merging of its classes is doubly regular. The goal of this paper is to study basic properties of this class of schemes. 
@article{ZNSL_2017_455_a9,
     author = {M. E. Muzychuk},
     title = {On {T-amorphous} association schemes},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {98--121},
     year = {2017},
     volume = {455},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2017_455_a9/}
}
TY  - JOUR
AU  - M. E. Muzychuk
TI  - On T-amorphous association schemes
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2017
SP  - 98
EP  - 121
VL  - 455
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2017_455_a9/
LA  - en
ID  - ZNSL_2017_455_a9
ER  - 
%0 Journal Article
%A M. E. Muzychuk
%T On T-amorphous association schemes
%J Zapiski Nauchnykh Seminarov POMI
%D 2017
%P 98-121
%V 455
%U http://geodesic.mathdoc.fr/item/ZNSL_2017_455_a9/
%G en
%F ZNSL_2017_455_a9
M. E. Muzychuk. On T-amorphous association schemes. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 31, Tome 455 (2017), pp. 98-121. http://geodesic.mathdoc.fr/item/ZNSL_2017_455_a9/

[1] E. Bannai, T. Ito, Algebraic Combinatorics, v. I, Association Schemes, Benjamin/Cummings Publ., Menlo Park, 1984 | MR | Zbl

[2] A. Hanaki, J. Terado, Frobenius–Schur theorem for association schemes, Manuscript

[3] A. Hanaki, “A condition on lengths of conjugacy classes and character degrees”, Osaka J. Math., 33:1 (1996), 207–216 | MR | Zbl

[4] D. G. Higman, “Coherent Algebras”, Linear Algebra and Its Applications, 93 (1987), 209–239 | DOI | MR | Zbl

[5] R. A. Horn, C. R. Johnson, Matrix analysis, Cambridge, 1985 | MR

[6] T. Ito, A. Munemasa, M. Yamada, “Amorphous association schemes over the Galois rings of characteristic 4”, European J. Combin., 12:6 (1991), 513–526 | DOI | MR | Zbl

[7] T. Ikuta, T. Ito, A. Munemasa, “On pseudo-automorphisms and fusions of an association scheme”, European J. Combin., 12 (1991), 317–325 | DOI | MR | Zbl

[8] C. Godsil, Association schemes, Lecture Notes, , 2005 https://www.math.uwaterloo.ca/~cgodsil/pdfs/assoc2.pdf

[9] J. J. Golfand, A. V. Ivanov, M. Klin, “Amorphic cellular rings”, Investigations in Algebraic Theory of Combinatorial Objects, eds. I. A. Faradz̆ev, et al., Kluwer, Dordrecht, 1994, 167–186 | DOI | Zbl

[10] J. Ma, “The non-existence of certain skew-symmetric amorphous association schemes”, European J. Combin., 31:7 (2010), 1671–1679 | DOI | MR | Zbl

[11] T. Feng, Q. Xiang, “Cyclotomic construction of skew Hadamard difference sets”, JCT(A), 119 (2012), 245–256 | MR | Zbl

[12] R. J. L. Oliver, “Gauss sums over finite fields and roots of unity”, Proc. Amer. Math. Soc., 139 (2011), 1273-1276 | DOI | MR | Zbl

[13] J. Putter, “Maximal sets of anti-commuting skew-symmetric matrices”, J. London Math. Soc., 42 (1967), 303–308 | DOI | MR | Zbl

[14] B. Weisfeiler (Ed.), On the construction and identification of graphs, Lect. Notes in Math., 558, 1976 | DOI

[15] P. H. Zieschang, Theory of association schemes, Springer Monographs in Mathematics, 283, Springer-Verlag, Berlin, 2005 | MR | Zbl