The Multiplicities of a Dual-thin Q-polynomial Association Scheme
Combinatorics
2012-08-27 v1
Abstract
Let Y denote a symmetric association scheme which is Q-polynomial with respect to an ordering E_0,...,E_D of the primitive idempotents. Bannai and Ito conjectured that the associated sequence of multiplicities m_0,...,m_D is unimodal. We prove that if Y is dual-thin in the sense of Terwilliger, then the sequence of multiplicities satisfies m_i <= m_{i+1} and m_i <= m_{D-i} for i < D/2.
Cite
@article{arxiv.math/9907079,
title = {The Multiplicities of a Dual-thin Q-polynomial Association Scheme},
author = {John S. Caughman and IV and Bruce E. Sagan},
journal= {arXiv preprint arXiv:math/9907079},
year = {2012}
}
Comments
5 pages