Premium
On spherical designs obtained from Q ‐polynomial association schemes
Author(s) -
Suda Sho
Publication year - 2011
Publication title -
journal of combinatorial designs
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.618
H-Index - 34
eISSN - 1520-6610
pISSN - 1063-8539
DOI - 10.1002/jcd.20278
Subject(s) - mathematics , idempotence , bounded function , association scheme , eigenvalues and eigenvectors , polynomial , embedding , combinatorics , constant (computer programming) , scheme (mathematics) , discrete mathematics , mathematical analysis , computer science , physics , quantum mechanics , artificial intelligence , programming language
We characterize that the image of the embedding of the Q ‐polynomial association scheme into the first eigenspace by primitive idempotent E 1 is a spherical t ‐design in terms of the Krein numbers. Furthermore, we show that the strengths of P ‐ and Q ‐polynomial schemes as spherical designs are bounded by a constant. Copyright © 2011 John Wiley & Sons, Ltd. 19:167‐177, 2011