1Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240, China 2Misakigaoka 2-8-21, Itoshima 819-1136, Japan 3Department of Mathematics Education, Aichi University of Education, Kariya 448-8542, Japan 4Research Center for Pure and Applied Mathematics, Graduate School of Information Sciences, Tohoku University, Sendai 980-8579, Japan
The electronic journal of combinatorics, Tome 22 (2015) no. 4
Motivated by the similarities between the theory of spherical $t$-designs and that of $t$-designs in $Q$-polynomial association schemes, we study two versions of relative $t$-designs, the counterparts of Euclidean $t$-designs for $P$- and/or $Q$-polynomial association schemes. We develop the theory based on the Terwilliger algebra, which is a noncommutative associative semisimple $\mathbb{C}$-algebra associated with each vertex of an association scheme. We compute explicitly the Fisher type lower bounds on the sizes of relative $t$-designs, assuming that certain irreducible modules behave nicely. The two versions of relative $t$-designs turn out to be equivalent in the case of the Hamming schemes. From this point of view, we establish a new algebraic characterization of the Hamming schemes.
1
Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240, China
2
Misakigaoka 2-8-21, Itoshima 819-1136, Japan
3
Department of Mathematics Education, Aichi University of Education, Kariya 448-8542, Japan
4
Research Center for Pure and Applied Mathematics, Graduate School of Information Sciences, Tohoku University, Sendai 980-8579, Japan
@article{10_37236_4889,
author = {Eiichi Bannai and Etsuko Bannai and Sho Suda and Hajime Tanaka},
title = {On relative \(t\)-designs in polynomial association schemes},
journal = {The electronic journal of combinatorics},
year = {2015},
volume = {22},
number = {4},
doi = {10.37236/4889},
zbl = {1329.05307},
url = {http://geodesic.mathdoc.fr/articles/10.37236/4889/}
}
TY - JOUR
AU - Eiichi Bannai
AU - Etsuko Bannai
AU - Sho Suda
AU - Hajime Tanaka
TI - On relative \(t\)-designs in polynomial association schemes
JO - The electronic journal of combinatorics
PY - 2015
VL - 22
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UR - http://geodesic.mathdoc.fr/articles/10.37236/4889/
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%A Hajime Tanaka
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%J The electronic journal of combinatorics
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Eiichi Bannai; Etsuko Bannai; Sho Suda; Hajime Tanaka. On relative \(t\)-designs in polynomial association schemes. The electronic journal of combinatorics, Tome 22 (2015) no. 4. doi: 10.37236/4889
