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• W2171569252 abstract "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." @default.
• W2171569252 created "2016-06-24" @default.
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• W2171569252 date "2015-12-23" @default.
• W2171569252 modified "2023-09-30" @default.
• W2171569252 title "On Relative $t$-Designs in Polynomial Association Schemes" @default.
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• W2171569252 doi "https://doi.org/10.37236/4889" @default.
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