Geodesic
A survey on tight Euclidean $t$-designs and tight relative $t$-designs in certain association schemes
Informatics and Automation, Geometry, topology, and applications, Tome 288 (2015), pp. 209-223

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

It is known that there is a close analogy between the two relations "Euclidean $t$-designs vs. spherical $t$-designs" and "relative $t$-designs in binary Hamming association schemes vs. combinatorial $t$-designs." We first look at this analogy and survey the known results, putting emphasis on the study of tight relative $t$-designs in certain $Q$-polynomial association schemes. We then specifically study tight relative $2$-designs on two shells in binary Hamming association schemes $H(n,2)$ and Johnson association schemes $J(v,k)$. The purpose of this paper is to convince the reader that there is a rich theory even for these special cases and that the time is ripe to study tight relative $t$-designs more systematically for general $Q$-polynomial association schemes. 
@article{TRSPY_2015_288_a13,
     author = {Eiichi Bannai and Etsuko Bannai and Yan Zhu},
     title = {A survey on tight {Euclidean} $t$-designs and tight relative $t$-designs in certain association schemes},
     journal = {Informatics and Automation},
     pages = {209--223},
     publisher = {mathdoc},
     volume = {288},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2015_288_a13/}
}
TY  - JOUR
AU  - Eiichi Bannai
AU  - Etsuko Bannai
AU  - Yan Zhu
TI  - A survey on tight Euclidean $t$-designs and tight relative $t$-designs in certain association schemes
JO  - Informatics and Automation
PY  - 2015
SP  - 209
EP  - 223
VL  - 288
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TRSPY_2015_288_a13/
LA  - en
ID  - TRSPY_2015_288_a13
ER  - 
%0 Journal Article
%A Eiichi Bannai
%A Etsuko Bannai
%A Yan Zhu
%T A survey on tight Euclidean $t$-designs and tight relative $t$-designs in certain association schemes
%J Informatics and Automation
%D 2015
%P 209-223
%V 288
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TRSPY_2015_288_a13/
%G en
%F TRSPY_2015_288_a13
Eiichi Bannai; Etsuko Bannai; Yan Zhu. A survey on tight Euclidean $t$-designs and tight relative $t$-designs in certain association schemes. Informatics and Automation, Geometry, topology, and applications, Tome 288 (2015), pp. 209-223. http://geodesic.mathdoc.fr/item/TRSPY_2015_288_a13/