A Note on Thin P-Polynomial and Dual-Thin Q-Polynomial Symmetric Association Schemes期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

A Note on Thin P-Polynomial and Dual-Thin Q-Polynomial Symmetric Association Schemes

Authors:	Garth A. Dickie Paul M. Terwilliger

Affiliation:	(1) Discrete Mathematics HG 9.53, University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands;(2) Department of Mathematics, University of Wisconsin, 480 Lincoln Drive, Madison, WI, 53706

Abstract:	Let Y denote a d-class symmetric association scheme, with d 3. We show the following: If Y admits a P-polynomial structure with intersection numbers p_ij^h and Y is 1-thin with respect to at least one vertex, then p_ll^l=0 p_liⁱ=0 1 i - 1. If Y admits a Q-polynomial structure with Krein parameters q_ij^h, and Y is dual 1-thin with respect to at least one vertex, then q_ll^l = 0 q_liⁱ = 01 i d-1.

Keywords:	Association scheme distance-regular graph intersection number Q-polynomial
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